Dissertations / Theses: 'Zeta'

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TSUMURA, Hirofumi, Kohji MATSUMOTO, and Yasushi KOMORI. "Multiple zeta values and zeta-functions of root systems." 日本学士院The Japan Academy, 2011. http://hdl.handle.net/2237/20333.

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Mijović, Vuksan. "Multifractal zeta functions." Thesis, University of St Andrews, 2017. http://hdl.handle.net/10023/10637.

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Multifractals have during the past 20 − 25 years been the focus of enormous attention in the mathematical literature. Loosely speaking there are two main ingredients in multifractal analysis: the multifractal spectra and the Renyi dimensions. One of the main goals in multifractal analysis is to understand these two ingredients and their relationship with each other. Motivated by the powerful techniques provided by the use of the Artin-Mazur zeta-functions in number theory and the use of the Ruelle zeta-functions in dynamical systems, Lapidus and collaborators (see books by Lapidus & van Frankenhuysen [32, 33] and the references therein) have introduced and pioneered use of zeta-functions in fractal geometry. Inspired by this development, within the past 7−8 years several authors have paralleled this development by introducing zeta-functions into multifractal geometry. Our result inspired by this work will be given in section 2.2.2. There we introduce geometric multifractal zeta-functions providing precise information of very general classes of multifractal spectra, including, for example, the multifractal spectra of self-conformal measures and the multifractal spectra of ergodic Birkhoff averages of continuous functions. Results in that section are based on paper [37]. Dynamical zeta-functions have been introduced and developed by Ruelle [63, 64] and others, (see, for example, the surveys and books [3, 54, 55] and the references therein). It has been a major challenge to introduce and develop a natural and meaningful theory of dynamical multifractal zeta-functions paralleling existing theory of dynamical zeta functions. In particular, in the setting of self-conformal constructions, Olsen [49] introduced a family of dynamical multifractal zeta-functions designed to provide precise information of very general classes of multifractal spectra, including, for example, the multifractal spectra of self-conformal measures and the multifractal spectra of ergodic Birkhoff averages of continuous functions. However, recently it has been recognised that while self-conformal constructions provide a useful and important framework for studying fractal and multifractal geometry, the more general notion of graph-directed self-conformal constructions provide a substantially more flexible and useful framework, see, for example, [36] for an elaboration of this. In recognition of this viewpoint, in section 2.3.11 we provide main definitions of the multifractal pressure and the multifractal dynamical zeta-functions and we state our main results. This section is based on paper [38]. Setting we are working unifies various different multifractal spectra including fine multifractal spectra of self-conformal measures or Birkhoff averages of continuous function. It was introduced by Olsen in [43]. In section 2.1 we propose answer to problem of defining Renyi spectra in more general settings and provide slight improvement of result regrading multifractal spectra in the case of Subshift of finite type.

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3

White, J. V. V. "Zeta functions of groups." Thesis, University of Oxford, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365745.

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Reyes, Ernesto Oscar. "The Riemann zeta function." CSUSB ScholarWorks, 2004. https://scholarworks.lib.csusb.edu/etd-project/2648.

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The Riemann Zeta Function has a deep connection with the distribution of primes. This expository thesis will explain the techniques used in proving the properties of the Rieman Zeta Function, its analytic continuation to the complex plane, and the functional equation that the the Riemann Zeta Function satisfies.

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EGAMI, SHIGEKI, and KOHJI MATSUMOTO. "ASYMPTOTIC EXPANSIONS OF MULTIPLE ZETA FUNCTIONS AND POWER MEAN VALUES OF HURWITZ ZETA FUNCTIONS." Cambridge University Press, 2002. http://hdl.handle.net/2237/10284.

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Firouzian, Bandpey Siamak. "Zeta functions of local orders." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=978669827.

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7

Andersson, Johan. "Summation formulae and zeta functions." Doctoral thesis, Stockholm : Department of Mathematics, Stockholm University, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-1074.

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Berman, Mark Nicholas. "Proisomorphic zeta functions of groups." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.424860.

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TSUMURA, HIROFUMI, KOHJI MATSUMOTO, and YASUSHI KOMORI. "ZETA-FUNCTIONS OF ROOT SYSTEMS." World Scientific Publishing, 2006. http://hdl.handle.net/2237/20355.

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Juchmes, Franziska. "Zeta Functions and Riemann Hypothesis." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-32363.

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In this thesis the zeta functions in analytic number theory are stud-ied. The distribution of primes and the connection between primes andzeta functions are discussed. Numerical results for linear combinationsof zeta functions are presented. These functions have a symmetric dis-tribution of zeros around the critical line.

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11

Matsumoto, Kohji. "Recent Developments in the Mean Square Theory of the Riemann Zeta and Other Zeta-Functions." Hindustan Book Agency & The Indian National Science Academy, 2000. http://hdl.handle.net/2237/20433.

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Horton, Matthew D. "Ihara zeta functions of irregular graphs." Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2006. http://wwwlib.umi.com/cr/ucsd/fullcit?p3206965.

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Thesis (Ph. D.)--University of California, San Diego, 2006.
Title from first page of PDF file (viewed May 10, 2006). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 88-89) and index.

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MATSUMOTO, KOHJI. "Functional equations for double zeta-functions." Cambridge University Press, 2004. http://hdl.handle.net/2237/10257.

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Kytmanov, Aleksandr, Simona Myslivets, and Nikolai Tarkhanov. "Zeta-function of a nonlinear system." Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2008/2679/.

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Given a system of entire functions in Cn with at most countable set of common zeros, we introduce the concept of zeta-function associated with the system. Under reasonable assumptions on the system, the zeta-function is well defined for all s ∈ Zn with sufficiently large components. Using residue theory we get an integral representation for the zeta-function which allows us to construct an analytic extension of the zeta-function to an infinite cone in Cn.

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Bäcklund, Pierre. "Automorphic distributions and Selberg zeta functions /." Uppsala, 2005. http://www.math.uu.se/research/pub/Backlundlic.pdf.

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Evseev, Anton. "Groups : uniformity questions and zeta functions." Thesis, University of Oxford, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.442941.

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McKenzie-Smith, Julian James. "Zeta-function methods in curved spacetimes." Thesis, University of Newcastle Upon Tyne, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275594.

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Snaith, Nina Claire. "Random matrix theory and zeta functions." Thesis, University of Bristol, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.322610.

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19

Snocken, Robert. "Zeta functions of groups and rings." Thesis, University of Southampton, 2014. https://eprints.soton.ac.uk/372833/.

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The representation growth of a T -group is polynomial. We study the rate of polynomial growth and the spectrum of possible growth, showing that any rational number α can be realized as the rate of polynomial growth of a class 2 nilpotent T -group. This is in stark contrast to the related subject of subgroup growth of T -groups where it has been shown that the set of possible growth rates is discrete in Q. We derive a formula for almost all of the local representation zeta functions of a T2-group with centre of Hirsch length 2. A consequence of this formula shows that the representation zeta function of such a group is finitely uniform. In contrast, we explicitly derive the representation zeta function of a specific T2-group with centre of Hirsch length 3 whose representation zeta function is not finitely uniform. We give formulae, in terms of Igusa's local zeta function, for the subring, left-, right- and two-sided ideal zeta function of a 2-dimensional ring. We use these formulae to compute a number of examples. In particular, we compute the subring zeta function of the ring of αintegers in a quadratic number field.

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20

Oh, Jangheon. "On Zeta Functions and Iwasawa Modules /." The Ohio State University, 1995. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487930304689598.

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21

Loeser, François. "Fonctions zeta locales d'igusa et singularites." Paris 7, 1988. http://www.theses.fr/1988PA077193.

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On etudie dans cette these les poles des fonctions zeta locales d'igusa (ou puissances complexes) associees a des fonctions complexes ou p-adiques. Dans le cas complexe on utilise la theorie de hodge. Dans le cas p-adique on relie les poles aux polynomes de bernstein et a la monodromie. On etudie aussi le cas de plusieurs fonctions. La these contient egalement un article sur le volume des tubes autour des singularites et un autre sur le polynome d'alexander des courbes planes projectives

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22

Heap, Winston. "Moments of the Dedekind zeta function." Thesis, University of York, 2013. http://etheses.whiterose.ac.uk/4669/.

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We study analytic aspects of the Dedekind zeta function of a Galois extension. Specifically, we are interested in its mean values. In the first part of this thesis we give a formula for the second moment of the Dedekind zeta function of a quadratic field times an arbitrary Dirichlet polynomial of length $T^{1/11-\epsilon}$. In the second part, we derive a hybrid Euler-Hadamard product for the Dedekind zeta function of an arbitrary number field. We rigorously calculate the $2k$th moment of the Euler product part as well as conjecture the $2k$th moment of the Hadamard product using random matrix theory. In both instances we are restricted to Galois extensions. We then conjecture that the $2k$th moment of the Dedekind zeta function of a Galois extension is given by the product of the two. By using our results from the first part of this thesis we are able to prove both conjectures in the case $k=1$ for quadratic fields. We also re-derive our conjecture for the $2k$th moment of quadratic Dedekind zeta functions by using a modification of the moments recipe. Finally, we apply our methods to general non-primitive $L$-functions and gain a conjecture regarding their moments. Our main idea is that, to leading order, the moment of a product of distinct $L$-functions should be the product of the individual moments of the constituent $L$-functions.

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23

Lutterbüse, Ralf. "Die Zeta-Kette des T-Zell-Rezeptors." Diss., lmu, 2001. http://nbn-resolving.de/urn:nbn:de:bvb:19-1838.

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24

松本, 耕二, 博文津村, Kohji Matsumoto, and Hirofumi Tsumura. "Functional relations for various multiple zeta-functions." 京都大学数理解析研究所, 2006. http://hdl.handle.net/2237/9657.

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25

Walker, George MacInnes. "Computing zeta functions of varieties via fibration." Thesis, University of Oxford, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.526126.

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26

Mohit, Satyagraha. "Zeta-functions of modular diagonal quotient surfaces." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2002. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/NQ65684.pdf.

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27

Skerstonaitė, Santa. "Joint universality for periodic Hurwitz zeta-functions." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2009. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2009~D_20090827_124913-17749.

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The aim of our work is to obtain joint universality theorems for periodic Hurwitz zeta-functions. We prove two joint universality theorems for periodic Hurwitz zeta-function. In the first theorems, the set L is linearly independent over the field of national numbers, then the periodic Hurwitz zeta-functions are universality. In the second joint universality theorem, we consider the use then parameter alpha corresponds general periodic sequence. Then the set L is linearly independent over the field of national numbers and the rank hypothesis in this theorem is weaker then that in A. Laurinčikas (2008) work. Then the second periodic Hurwitz zeta-functions are universal too.
Magistro darbe yra nagrinėjamas Hurvico dzeta funkcijų rinkinio jungtinis universalumas. Yra įrodytos dvi jungtinės universalumo teoremos. Pirmoji teorema tvirtina, kad jei aibė L yra tiesiškai nepriklausoma virš racionaliųjų skaičių kūno, tai periodinės Hurvico dzeta funkcijos yra universalios. Ši teorema žymiai susilpnina sąlygas, kurioms esant, buvo gautas analogiškas rezultatas A. Javtoko ir A. Laurinčiko 2008 m. darbe. Antroje teoremoje yra nagrinėjamas atvejis, kai kiekvieną skaičių alpha atitinka periodinių sekų rinkinys. Kai sistema L yra tiesiškai nepriklausoma virš racionaliųjų skaičių kūno ir galioja vieno rango tipo sąlyga, silpnesnė negu A. Laurinčiko darbe (2008), tai periodinių Hurvico dzeta funkcijų rinkinys yra taip pat universalus.

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28

Marshall, Kevin P. "The lower chromospheres of #zeta# aurigae stars." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.360849.

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29

Paajanen, Pirita Maria. "Zeta functions of groups and arithmetic geometry." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.419325.

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30

Musser, Jason. "Higher Derivatives of the Hurwitz Zeta Function." TopSCHOLAR®, 2011. http://digitalcommons.wku.edu/theses/1093.

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The Riemann zeta function ζ(s) is one of the most fundamental functions in number theory. Euler demonstrated that ζ(s) is closely connected to the prime numbers and Riemann gave proofs of the basic analytic properties of the zeta function. Values of the zeta function and its derivatives have been studied by several mathematicians. Apostol in particular gave a computable formula for the values of the derivatives of ζ(s) at s = 0. The Hurwitz zeta function ζ(s,q) is a generalization of ζ(s). We modify Apostolʼs methods to find values of the derivatives of ζ(s,q) with respect to s at s = 0. As a consequence, we obtain relations among certain important constants, the generalized Stieltjes constants. We also give numerical estimates of several values of the derivatives of ζ(s,q).

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31

Černigova, Sondra. "Moment problem for the periodic zeta-function." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2014~D_20141111_114553-36360.

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In the thesis, problems related to the moments of the periodic zeta-function are considered. The aim of the thesis is to obtain asymptotic formulae for some analytic objects related to the periodic zeta-function. The problems are the following: 1. To prove the Atkinson-type formula with a new error term in the critical strip for the periodic zeta-function with rational parameter. 2. To prove a mean square formula for the error term in the Atkinson-type formula on the critical line for the periodic zeta-function. 3. To prove a mean square formula for the error term in the Atkinson-type formula in the critical strip for the periodic zeta-function. 4. To obtain an asymptotic formula for the fourth power moment of the periodic zeta-function.
Disertacijos tyrimo objektas yra periodinė dzeta funkcija. Mokslinė problema - šios funkcijos momentų problema. Darbo tikslas - įrodyti asimptotines formules periodinės funkcijos momentams bei kai kuriems objektams, susijusiems su šios funkcijos momentais. Darbo uždaviniai yra šie: 1. Įrodyti Atkinsono tipo formulę su korektišku liekamuoju nariu kritinėje juostoje periodinei dzeta funkcijai su racionaliuoju parametru. 2. Įrodyti Atkinsono tipo formulės periodinei dzeta funkcijai kritinėje tiesėje vidurkio formulę liekamojo nario modulio kvadratui. 3. Įrodyti Atkinsono tipo formulės periodinei dzeta funkcijai kritinėje juostoje vidurkio formulę liekamojo nario modulio kvadratui. 4. Gauti asimptotinę formulę periodinės dzeta funkcijos ketvirtajam momentui.

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32

Mengue, Jairo Krás. "Zeta-medidas e princípio dos grandes desvios." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2010. http://hdl.handle.net/10183/26002.

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Seguindo os trabalhos de William Parry e Mark Pollicott, analisamos expressões de funções zeta dinâmicas e construímos probabilidades envolvendo somas em órbitas periódicas, que chamamos de zeta-medidas. Mostramos que as zeta-medidas são ferramentas úteis para aproximar o equilíbrio de um potencial Holder e que podem ser usadas para aproximar a probabilidade maximizante. Para alguns casos, mostramos que esta convergência satisfaz um princípio dos grandes desvios sem assumir unicidade da probabilidade maximizante. Como as iterações do Operador de Ruelle podem ser usadas para aproximar o equilíbrio de um potencial Holder, tomando um limite em duas variáveis, mostramos que elas podem ser usadas para aproximar a probabilidade maximizante. Supondo a unicidade da probabilidade maximizante, mostramos que esta convergência satisfaz um princípio dos grandes desvios com o mesmo funcional obtido por Baraviera-Lopes-Thieullen, para as medidas de equilíbrio. Mostramos antes que este funcional difere do obtido para zeta-medidas. Em uma seção independente, construímos um ponto cujo w-limite não contém pontos periódicos. Este w-limite pode ser aproximado exponencialmente em N por órbitas periódicas de tamanho menor ou igual a N.
We follow the works of William Parry and Mark Pollicott considering expressions of dinamical zeta functions and construct probabilities over sum on periodic orbits, that we call zeta-measures. We show that zeta-measures are useful tools to approximate the equilibrium measure of a H¨older potential and also they can be used to approximate the maximizing measure. In some cases, we show that this convergence satisfies a Large Deviation Principle (LDP) without assuming unicity of the maximizing measure. The Ruelle Operator can be used to approximate the equilibrium measure of a H¨older potential, so taking a limit on two variables, we show that they can be used to aproximate the maximizing measure. When there is a unique maximizing measure, we show that this convergence satisfies a LDP with the same functional given by Baraviera-Lopes-Thieullen, for equilibrium measures. We have shown before that this functional isn’t the same for zeta-measures. In a independent section we construct a point such that the w-limit set doesn’t have periodic points. This w-limit set can be approximate exponencialy in N by periocic orbits with period smaller than N.

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33

Tamiozzo, Matteo. "Zeta and L-functions of elliptic curves." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/7385/.

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In questa tesi si studiano alcune proprietà fondamentali delle funzioni Zeta e L associate ad una curva ellittica. In particolare, si dimostra la razionalità della funzione Zeta e l'ipotesi di Riemann per due famiglie specifiche di curve ellittiche. Si studia poi il problema dell'esistenza di un prolungamento analitico al piano complesso della funzione L di una curva ellittica con moltiplicazione complessa, attraverso l'analisi diretta di due casi particolari.

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Diaz-Vargas, Javier Arturo 1952. "On zeros of characteristic p zeta functions." Diss., The University of Arizona, 1996. http://hdl.handle.net/10150/290585.

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The location and multiplicity of the zeros of zeta functions encode interesting arithmetic information. We study characteristic p zeta functions of Carlitz and Goss. We present a simpler proof of the fact that "non-trivial" zeros of a characteristic p zeta function satisfy Goss' analogue of the Riemann Hypothesis for F(q)[T]. We also prove simplicity of these zeros, and give partial results for F(q)[T] where q is not necessarily prime. Then we focus on "trivial" zeros, but for characteristic p zeta functions for general function fields over finite fields. Here, we prove a theorem on zeros at negative integers for characteristic p zeta functions, showing more vanishing than that suggested by naive analogies. We also compute some concrete examples providing the extra vanishing, when the class number is more than one. Finally, we give an application of these results related to the non-vanishing of certain class group components for cyclotomic function fields. In particular, we give examples of function fields, where all the primes of degree more than two are "irregular", in the sense of the Drinfeld-Hayes cyclotomic theory.

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35

Guariglia, Emanuel. "Fractional derivative of the riemann zeta function." Doctoral thesis, Universita degli studi di Salerno, 2017. http://hdl.handle.net/10556/2611.

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2015 - 2016
In this work of thesis, the Riemann zeta function was studied by using an unconventional approach. The reason for choosing this approach was to explore the many applications that the Riemann zeta has not only in pure mathematics, but also in tangential fields of theoretical physics and engineering. The use of fractional calculus allowed the computation of the α-order fractional derivative ζ(α). The biggest difficulty was represented by the fractional differentiation in the complex plane. In particular, two generalizations of the fractional derivative (Caputo derivative and Grünwald-Letnikov derivative) to the complex field were used in this thesis. The first chapter includes several preliminaries on the analytics number theory and on fractional calculus. In the second chapter the computation of ζ(α) is given together with its convergence. ζ(α) is expressed as a complex series and represents a fractional generalization to the integer derivative of ζ. In fact, by replacing in the right hand side the fractional exponent α with the integer exponent k, ζ(α) becomes ζ(k). Some properties of this derivative were obtained in order to show its chaotic decay to zero and several links with the analytic number theory. The third chapter presents the computation of the functional equation together with some simplified versions, in accordance with the classical theory of the Riemann zeta function. Since the Caputo-Ortigueira fractional derivative does not satisfy the generalized Leibniz rule, the generalization of the GrünwaldLetnikov fractional derivative to complex plane must be introduced. The desired functional equation was obtained by starting from the asymmetric from of the functional equation of ζ. Further properties relating to this equation are proposed and comprehensively discussed in this chapter. Generalizations of this fractional derivative were obtained by introducing the series of Dirichlet, the Hurwitz zeta function and the Lerch zeta function. By using the generalization of the Grünwald-Letnikov fractional derivative, generalizations of the functional equations associated to ζ(α) are given. In particular, the functional equation associated to the fractional derivative of the zeta Lerch have supplied new results, and new horizons for research seem to open in the fractional calculus functional. Additionally, an integral representation of ζ(α), in terms of numbers of Bernoulli is also presented. All of the aforementioned results are in agreement with the classical theory of Riemann zeta function. In the fourth chapter, the link between ζ(α) and the distribution of prime numbers is discussed by using the Euler products. The logarithmic fractional derivative of the Riemann ζ function provides a partial result in this direction. The introduction of the zeta function Dirichlet and the computation of its fractional derivative have given a better knowledge of ζ(α) in the critical strip 0 α, hence ζ(α) and η(α) suggest the strip α < Re s < 1+α as a fractional counterpart of the critical strip. This result shows that there is a clear link between this function and the distribution of prime numbers. The fifth chapter provides an application of two signal processing networks associated to η(α). The spectral properties of both ζ(α) and η(α) are given and the symmetry is shown. The fractional derivative of the Riemann ζ function seems to have many promising applications in pure and applied mathematics. For instance, an example is presented based on the knowledge that complex functions can be studied in a suitable function space in order to solve a given problem. This is represented by the Hilbert spaces of entire functions, in which de Branges had linked the Riemann hypothesis with a positivity condition on these particular function spaces. It is assumed that by taking into account the interest that the fractional calculus has had in recent years, ζ(α) has the potential to bring interesting results in fractional Hilbert spaces. [edited by author]
In questo lavoro di tesi, la funzione zeta di Riemann è stata studiata attraverso un approccio non convenzionale. Le ragioni di tale scelta risiedono nelle molteplici applicazioni che tale funzione ha non sono nella matematica pura ma anche in fisica teorica ed ingegneria. L'uso del fractional calculus ha permesso il calcolo della derivata frazionaria ζ(α). La maggiore difficoltà è stata rappresentata della differenziazione nel piano complesso. In particolare, due generalizzazioni della derivata frazionaria (derivata di Caputo e derivata di Grünwald-Letnikov) al campo complesso sono state utilizzate in questa tesi. Il primo capitolo include diverse nozioni preliminari sulla teoria analitica dei numeri e sul fractional calculus. Nel secondo capitolo, il calcolo di ζ(α) è stato effettuato e il suo semipiano di convergenza studiato. ζ(α) è espresso come una serie complessa e rappresenta la generalizzazione frazionaria della derivata intera di ζ. Alcune proprietà di questa derivata frazionaria sono state ottenute al fine di mostrare sia il suo decadimento caotico a zero che i diversi collegamenti con la teoria analitica dei numeri. Il terzo capitolo è dedicato all'equazione funzionale insieme con alcune sue versioni semplificate, in accordo con la teoria classica della funzione zeta di Riemann. Siccome la derivata di Caputo-Ortigueira non soddisfa la regola generalizzata di Leibniz, la generalizzazione della derivata di Grünwald-Letnikov al piano complesso è stata introdotta. L'equazione funzionale cercata è così dedotta semplicemente dalla forma asimmetrica dell'equazione funzionale della ζ. Ulteriori proprietà di questa equazione sono fornite e discusse in questo capitolo. Alcune generalizzazioni di questa derivata frazionaria sono state ottenute introducendo la funzione zeta di Hurwitz, la serie di Dirichlet e la funzione zeta di Lerch. In questo modo, l'equazione funzionale di ζ(α) è generalizzata ai tre casi sopra esposti. In particolare, l'equazione funzionale della zeta di Lerch ha fornito sorprendenti risultati e nuovi orizzonti di ricerca sembrano aprirsi nelle applicazioni del fractional calculus in analisi funzionale. Inoltre, una rappresentazione integrale di ζ(α) in termini di numeri di Bernoulli è presentata. Tutti I risultati sopra descritti sono in accordo con la teoria classica della funzione zeta di Riemann. Nel quarto capitolo, il legame tra ζ(α) e la distribuzione dei numeri primi è discussa introducendo i prodotti euleriani. La derivata frazionaria logaritmica della ζ di Riemann fornisce un risultato parziale in questa direzione. L'introduzione della funzione eta di Dirichlet ed il calcolo della sua derivata frazionaria hanno fornito una migliore comprensione di ζ(α) nella striscia critica 0 α, ζ(α) e η(α) suggeriscono chiaramente di interpretare la striscia α < Re s < 1+α come la controparte frazionaria della striscia critica. Questo risultato mostra un chiaro legame tra ζ(α) e la distribuzione dei numeri primi. Il quinto capitolo mostra il comportamento di due reti basate su η(α). Le proprietà spettrali sia di ζ(α) che di η(α) sono derivate e la loro simmetria è mostrata. La derivata frazionaria della ζ di Riemann sembra avere molte promettenti applicazioni sia nelle matematiche pure che applicate. Alcune funzioni complesse possono essere studiate in un opportuno spazio funzionale al fine di risolvere un dato problema, come nel caso degli spazi di Hilbert per le funzioni intere. E' ben noto in letteratura come de Branges ha connesso l'ipotesi di Riemann con una condizione di positività su questi particolari spazi di funzioni. Tenendo conto di tutto ciò e del crescente interesse dei ricercatori verso il fractional calculus negli ultimi anni, ζ(α) potrebbe avere diverse applicazioni negli spazi di Hilbert frazionari. [a cura dell'autore]
XV n.s.

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36

Satou, Nobuo. "AN ENHANCEMENT OF THE ZAGIER CONJECTURE." 京都大学 (Kyoto University), 2017. http://hdl.handle.net/2433/225380.

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37

Thomas, Christian [Verfasser], and Hermann [Akademischer Betreuer] Pavenstädt. "Charakterisierung der Interaktion des KIBRA-Proteins mit der Protein-Kinase M Zeta (PKM Zeta) / Christian Thomas ; Betreuer: Hermann Pavenstädt." Münster : Universitäts- und Landesbibliothek Münster, 2015. http://d-nb.info/1138279900/34.

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Merrill, Katherine J. "Ramanujan's Formula for the Riemann Zeta Function Extended to L-Functions." Fogler Library, University of Maine, 2005. http://www.library.umaine.edu/theses/pdf/MerrillKJ2005.pdf.

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39

Steuding, Jörn. "On simple zeros of the Riemann zeta-function." [S.l. : s.n.], 1999. http://deposit.ddb.de/cgi-bin/dokserv?idn=95589820X.

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40

Hussner, Thomas. "The p-adic zeta functions of Chevalley groups." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=971952256.

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41

Gauthier, Paul M., and Nikolai Tarkhanov. "A covering property of the Riemann zeta-function." Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2008/2668/.

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For each compact subset K of the complex plane C which does not surround zero, the Riemann surface Sζ of the Riemann zeta function restricted to the critical half-strip 0 < Rs < 1/2 contains infinitely many schlicht copies of K lying ‘over’ K. If Sζ also contains at least one such copy, for some K which surrounds zero, then the Riemann hypothesis fails.

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42

Karaliūnaitė, Julija. "Value distribution theorems for the periodic zeta-function." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2010. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2010~D_20100915_162405-31358.

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In the thesis, the Atkinson formula for the periodic zeta-function on the critical line and the critical strip, and limit theorems in the sense of weak convergence of probability measures in various spaces are considered. The aim of the thesis is to solve the following problems: 1. To obtain the Atkinson formula on the critical line for the periodic zeta-function. 2. To obtain the Atkinson formula in the critical strip for the periodic zeta-function. 3. To prove limit theorems on the complex plane in the sense of weak convergence for the periodic zeta-function. 4. To prove limit theorems in the space of analytic functions for the periodic zeta-function. To solve them analytical and probabilistic methods are applied. For the proof of Atkinson formula, we use properties of the error term in the Dirichlet divisor problem and classical Voronoi formula. For the proof of limit theorems, the theory of weak convergence of probability measures, in particular, the Prokhorov's theory is applied. All results obtained in the thesis are new. The Atkinson formula for periodic zeta-function was not known. The same is true for limit theorems for periodic zeta-function. The Atkinson formula gives the explicit formula for the error term in the asymptotic formula for the first moment. This result is not only interesting itself but also has a series of applications, for example, in the investigation of higher moments. Probabilistic limit theorems are used for the characterization of... [to full text]
Darbe nagrinėjama periodinės dzeta funkcijos antrojo momento liekamojo nario išreikštinis pavidalas ir šios funkcijos asimptotinio elgesio charakterizacija ribinių teoremų silpnojo tikimybinių matų konvergavimo prasmė įvairiose erdvėse pagalba. Darbo uždaviniai yra šie: 1. Įrodyti Atkinsono formulę periodinai dzeta funkcijai kritinėje tiesėje. 2. Įrodyti Atkinsono formulę periodinai dzeta funkcijai kritinėje juostoje. 3. Įrodyti ribinę teoremą su ribinio mato išreikštiniu pavidalu kompleksinėje plokštumoje periodinei dzeta funkcijai. 4. Įrodyti ribinę teoremą su ribinio mato išreikštiniu pavidalu analizinių funkcijų erdvėje periodinei dzeta funkcijai. Atkinsono formulė duoda momentų asimptotinės formulės liekamojų narių išreikštinį pavidalą. Tai ne tik įdomus, bet ir turintis rimtų pritaikymų, pavyzdžiui, tiriant aukštesniuosius momentus, rezultatas. Tikimybinės ribinės teoremos charakterizuoja dzeta funkcijų asimptotinio elgesio reguliarumą. Be to, buvo pastebėta, kad tokios teoremos yra svarbiausia dzeta funkcijų universalumo įrodymo grandis. Periodinė dzeta funkcija nėra klasikinė, ji yra Rymano (Riemann) dzeta funkcijos apibendrinimas, tačiau ji pasirodo įvairiuose analizinės skaičių teorijos uždaviniuose. Pavyzdžiui, ji įeina į Hurvico (Hurvitz) ir Lercho (Lerch) dzeta funkcijų antrojo momento parametro atžvilgiu asimptotinę formulę. Iš kitos pusės, darbų, skirtų periodinei dzeta funkcijai, yra nedaug, aukščiau minėti autoriai daugiausia dėmesio skyrė... [toliau žr. visą tekstą]

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Grigutis, Andrius. "Value distribution of Lerch and Selberg zeta-functions." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2012. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2012~D_20121227_085912-23915.

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The doctoral dissertation contains the material of scientific investigations done in 2008-2012 in the Faculty of Mathematics and Informatics at Vilnius University. The dissertation includes new theorems for the value distribution of Lerch and Selberg zeta-functions and computer calculations performed using the computational software program MATHEMATICA. The dissertation consists of the introduction, 3 chapters, the conclusions and the references. The results of the thesis are published in three scientific articles in Lithuanian and foreign journals, reported in scientific conferences in Lithuania and abroad and at the seminars of the department. In the first chapter, the limit theorems for several cases of the Lerch zeta-functions are proved. In the 1940s, Selberg proved that suitably normalized logarithm of modulus of the Riemann zeta-function on the critical line has a standard normal distribution. Selberg's proof was based on the Euler product; however, in general, Lerch zeta-functions have no Euler product. In the second chapter, the theorem concerning the zero distribution of the Lerch transendent function is proved, and computer calculations of zeros in the region Re(s)>1 are performed using MATHEMATICA. In the third chapter, the monotonicity properties of Selberg zeta-functions are investigated. Monotonicity of these two functions is directly related to the location of zeros in the critical strip. The results are compared to the monotonicity... [to full text]
Disertaciją sudaro mokslinių tyrimų medžiaga, kurie atlikti 2008 -2012 metais Vilniaus universitete Matematikos ir informatikos fakultete. Disertacijoje įrodomos naujos teoremos apie Lercho ir Selbergo dzeta funkcijų reikšmių pasiskirstymą, atliekami kompiuteriniai skaičiavimai matematine programa MATHEMATICA. Disertaciją sudaro įvadas, 3 skyriai, išvados ir literatūros sąrašas. Disertacijos rezultatai atspausdinti trijuose moksliniuose straipsniuose, Lietuvos ir užsienio žurnaluose, pristatyti Lietuvoje ir užsienyje vykusiose mokslinėse konferencijose bei katedros seminarų metu. Pirmajame skyriuje įrodinėjamos ribinės teoremos Lercho dzeta funkcijai. Praėjusio šimtmečio ketvirtame dešimtmetyje Selbergas įrodė, kad tinkamai normuotas Rymano dzeta funkcijos logaritmas ant kritinės tiesės turi standartinį normalųjį pasiskirstymą. Selbergo įrodymas rėmėsi Oilerio sandauga, kuria turi Rymano dzeta funkcija, bet bendru atveju jos neturi Lercho dzeta funkcija. Antrajame skyriuje įrodoma teorema apie Lercho transcendentinės funkcijos nulių įvertį vertikaliose kompleksinės plokštumos juostose bei atliekami kompiuteriniai nulių skaičiavimai srityje Re(s)>1 programa MATHEMATICA. Trečiajame skyriuje nagrinėjamos dviejų Selbergo dzeta funkcijų monotoniškumo savybės, kurios yra tiesiogiai susijusios su šių funkcijų nulių išsidėstymu kritinėje juostoje. Monotoniškumo savybės lyginamos su Rymano dzeta funkcijos monotoniškumo savybėmis ir nulių išsidėstymu, kuris yra viena didžiausių... [toliau žr. visą tekstą]

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Račkauskienė, Santa. "Joint universality of zeta-functions with periodic coefficients." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2012. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2012~D_20121214_110729-14777.

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In the thesis, the joint universality of periodic Hurwitz zeta-functions as well as that jointly with the Riemann zeta-functions of normalized cusp forms is obtained.
Darbe yra įrodomas jungtinis universalumas periodinėms Hurvico dzeta funkcijoms, taip pat bendras universalumas su Rymano dzeta funkcija ir normuotų parabolinių formų dzeta funkcija.

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45

Clare, B. "Nonstandard Mathematics and New Zeta and L-Functions." Thesis, University of Nottingham, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.519430.

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46

Tsumura, H., K. Matsumoto, and Y. Komori. "Functional relations for zeta-functions of root systems." World Scientific Publishing, 2009. http://hdl.handle.net/2237/20353.

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Steuding, Rasa, Jörn Steuding, Kohji Matsumoto, Antanas Laurinčikas, and Ramūnas Garunkštis. "Effective uniform approximation by the Riemann zeta-function." Department of Mathematics of the Universitat Autònoma de Barcelona, 2010. http://hdl.handle.net/2237/20429.

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48

Turner, S. M. "Hasse-Weil zeta functions for linear algebraic groups." Thesis, University of Glasgow, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318888.

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49

Cang, Shuang. "New asymptotic formulas for the Reimann zeta function." Thesis, University of Abertay Dundee, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.339242.

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50

Livingstone, Boomla Alice Jane. "Selmer groups, zeta elements and refined Stark conjectures." Thesis, King's College London (University of London), 2018. https://kclpure.kcl.ac.uk/portal/en/theses/selmer-groups-zeta-elements-and-refined-stark-conjectures(0ecef088-5829-4e5b-a35d-974c505136d9).html.

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In this thesis we study explicit connections between the values at s = 0 of the higher derivatives of Dirichlet L-functions and the higher Fitting ideals of Selmer groups of the multiplicative group over finite abelian extensions of number fields. We also prove new structural results for such Selmer groups, showing that their higher Fitting ideals admit natural direct sum decompositions. The first of our main results allows us to show that certain canonical invariants that are associated to (generalised) Rubin-Stark elements by Valli`eres in [28] can be completely, though in general only conjecturally, described in terms of the higher Fitting ideals of the Selmer groups of Gm. Following on from this observation, we then formulate a refined conjecture, which ex-tends the existing theory of abelian Stark conjectures in two key ways. Firstly, our conjecture deals for the first time in a consistent way with L-functions that do not necessarily have ‘minimal’ order of vanishing at s = 0 and secondly it includes an important ‘boundary case’ that has been excluded from all previous formulations of conjectures in this area. We also present evidence, both theoretic and numerical, for the conjectures that we formulate. In particular, we prove that our conjectures would follow from the validity of the relevant special case of equivariant Tamagawa number conjecture and are therefore, for example, unconditionally true in the classical setting of abelian extensions of Q.

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Dissertations / Theses on the topic 'Zeta'

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