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Dissertations / Theses on the topic 'Mathematics ; Number theory ; Analytic number theory'

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Published: 4 June 2021

Last updated: 6 February 2022

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1

Buchanan, Dan Matthews. "Analytic Number Theory and the Prime Number Theorem." Youngstown State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1525451327211365.

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2

Maynard, James. "Topics in analytic number theory." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:3bf4346a-3efe-422a-b9b7-543acd529269.

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In this thesis we prove several different results about the number of primes represented by linear functions. The Brun-Titchmarsh theorem shows that the number of primes which are less than x and congruent to a modulo q is less than (C+o(1))x/(phi(q)log{x}) for some value C depending on log{x}/log{q}. Different authors have provided different estimates for C in different ranges for log{x}/log{q}, all of which give C>2 when log{x}/log{q} is bounded. We show in Chapter 2 that one can take C=2 provided that log{x}/log{q}> 8 and q is sufficiently large. Moreover, we also produce a lower bound of s

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3

Guo, Charng Rang. "On analytic number theory." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357394.

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4

Dyke, Steven Douglas. "Topics in analytic number theory." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334817.

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5

Irving, Alastair James. "Topics in analytic number theory." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:40f5511c-af6b-4215-b1ab-97f203e8936b.

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In this thesis we prove several results in analytic number theory. 1. We show that there exist 3-digit palindromic primes in base b for a set of b having density 1 and that if b is sufficiently large then there is a $3$-digit palindrome in base b having precisely two prime factors. 2. We prove various estimates for averages of sums of Kloosterman fractions over primes. The first of these improves previous results of Fouvry-Shparlinski and Baker. 3. By using the q-analogue of van der Corput's method to estimate short Kloosterman sums we study the divisor function in an arithmetic progression to

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6

Baker, Liam Bradwin. "Analytic methods in combinatorial number theory." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/98017.

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Thesis (MSc)--Stellenbosch University, 2015<br>ENGLISH ABSTRACT : Two applications of analytic techniques to combinatorial problems with number-theoretic flavours are shown. The first is an application of the real saddle point method to derive second-order asymptotic expansions for the number of solutions to the signum equation of a general class of sequences. The second is an application of more elementary methods to yield asymptotic expansions for the number of partitions of a large integer into powers of an integer b where each part has bounded multiplicity.<br>AFRIKAANSE OPSOMMING :

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7

Powell, Kevin James. "Topics in Analytic Number Theory." BYU ScholarsArchive, 2009. https://scholarsarchive.byu.edu/etd/2084.

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The thesis is in two parts. The first part is the paper “The Distribution of k-free integers” that my advisor, Dr. Roger Baker, and I submitted in February 2009. The reader will note that I have inserted additional commentary and explanations which appear in smaller text. Dr. Baker and I improved the asymptotic formula for the number of k-free integers less than x by taking advantage of exponential sum techniques developed since the 1980's. Both of us made substantial contributions to the paper. I discovered the exponent in the error term for the cases k=3,4, and worked the case k=3 completely

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8

Walker, Aled. "Topics in analytic and combinatorial number theory." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:0d48a697-fd7a-4aca-bebe-4806322bdbbd.

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In this thesis we consider three different issues of analytic number theory. Firstly, we investigate how residues modulo q may be expressed as products of small primes. In Chapter 1, we work in the regime in which these primes are less than q, and present some partial results towards an open conjecture of Erdös. In Chapter 2, we consider the kinder regime in which these primes are at most q<sup>C</sup> , for some constant C that is greater than 1. Here we reach an explicit version of Linnik's Theorem on the least prime in an arithmetic progression, saving that we replace 'prime' with 'product

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9

Mullen, Woodford Roger. "Partitions into prime powers and related divisor functions." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/1246.

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In this thesis, we will study a class of divisor functions: the prime symmetric functions. These are polynomials over Q in the so-called elementary prime symmetric functions, whose values lie in Z. The latter are defined on the nonnegative integers and take the values of the elementary symmetric functions applied to the multi-set of prime factors (with repetition) of an integer n. Initially we look at basic properties of prime symmetric functions, and consider analogues of questions posed for the usual sum of proper divisors function, such as those concerning perfect numbers or Aliquot sequen

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10

Wang, Stephen. "Zeta Function Regularization and its Relationship to Number Theory." Digital Commons @ East Tennessee State University, 2021. https://dc.etsu.edu/etd/3895.

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While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and

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11

Lennon, Craig. "On the likely number of stable marriages." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1194991095.

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12

Anglin, William Sherron Raymond. "The nature of solutions in mathematics /." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=72100.

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What constitutes an adequate solution to a mathematical problem? When is an adequate solution a 'good' solution? In this thesis I consider these questions in relation to two Diophantine equations, namely, x$ sp2$ + k = y$ sp3$ and 6y$ sp2$ = x(x + 1)(2x + 1). The first dates back to Diophantus himself (c. 250 AD) while the second can be traced to a puzzle proposed by Edouard Lucas in 1875. Each of these equations has attracted a number of solutions and each solution reveals something about its era. An examination and comparison of these solutions will give us an opportunity to reflect on some

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13

Moore, Daniel Ross. "An Intrinsic Theory of Smooth Automorphic Representations." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1524174589105537.

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14

Butler, Steven Kay. "Bounding the Number of Graphs Containing Very Long Induced Paths." Diss., CLICK HERE for online access, 2003. http://contentdm.lib.byu.edu/ETD/image/etd158.pdf.

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15

Bredberg, Johan. "On large gaps between consecutive zeros, on the critical line, of some zeta-functions." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:3e744bbd-c947-405c-b519-4808c8c5a73e.

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In this thesis we extend a method of Hall $[30, 34]$ which he used to show the existence of large gaps between consecutive zeros, on the critical line, of the Riemann zeta-function $zeta(s)$. Our modification involves introducing an "amplifier" and enables us to show the existence of gaps between consecutive zeros, on the critical line at height $T,$ of $zeta(s)$ of length at least $2.766 x (2pi/log{T})$. To handle some integral-calculations, we use the article $[44]$ by Hughes and Young. Also, we show that Hall's strategy can be applied not only to $zeta(s),$ but also to Dirichlet $L$-functio

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16

Lau, Yuk-kam, and 劉旭金. "Error terms in the summatory formulas for certain number-theoretic functions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B31238804.

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17

Lau, Yuk-kam. "Error terms in the summatory formulas for certain number-theoretic functions /." Hong Kong : University of Hong Kong, 1999. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20897509.

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18

Harper, John-Paul. "The class number one problem in function fields." Thesis, Stellenbosch : Stellenbosch University, 2003. http://hdl.handle.net/10019.1/53619.

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Thesis (MComm)--Stellenbosch University, 2003.<br>ENGLISH ABSTRACT: In this dissertation I investigate the class number one problem in function fields. More precisely I give a survey of the current state of research into extensions of a rational function field over a finite field with principal ring of integers. I focus particularly on the quadratic case and throughout draw analogies and motivations from the classical number field situation. It was the "Prince of Mathematicians" C.F. Gauss who first undertook an in depth study of quadratic extensions of the rational numbers and the corre

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19

Bongiovanni, Alex. "Problems with power-free numbers and Piatetski-Shapiro sequences." Kent State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1618331559201676.

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20

Nyqvist, Robert. "Algebraic Dynamical Systems, Analytical Results and Numerical Simulations." Doctoral thesis, Växjö : Växjö University Press, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1142.

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21

Rothlisberger, Matthew Samuel. "Ergodic and Combinatorial Proofs of van der Waerden's Theorem." Scholarship @ Claremont, 2010. http://scholarship.claremont.edu/cmc_theses/14.

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Followed two different proofs of van der Waerden's theorem. Found that the two proofs yield important information about arithmetic progressions and the theorem. van der Waerden's theorem explains the occurrence of arithmetic progressions which can be used to explain such things as the Bible Code.

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22

Myerson, Simon L. Rydin. "Systems of forms in many variables." Thesis, University of Oxford, 2016. http://ora.ox.ac.uk/objects/uuid:a9932e90-4784-466a-a694-d387c1228533.

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We consider systems of polynomial equations and inequalities to be solved in integers. By applying the circle method, when the number of variables is large and the system is geometrically well-behaved we give an asymptotic estimate for the number of solutions of bounded size. In the case of R homogeneous equations having the same degree d, a classic theorem of Birch provides such an estimate provided the number of variables is R(R+1)(d-1)2<sup>d-1</sup>+R or greater and the system is nonsingular. In many cases this conclusion has been improved, but except in the case of diagonal equations the

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23

Krohne, Edward. "Continuous Combinatorics of a Lattice Graph in the Cantor Space." Thesis, University of North Texas, 2016. https://digital.library.unt.edu/ark:/67531/metadc849680/.

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We present a novel theorem of Borel Combinatorics that sheds light on the types of continuous functions that can be defined on the Cantor space. We specifically consider the part X=F(2ᴳ) from the Cantor space, where the group G is the additive group of integer pairs ℤ². That is, X is the set of aperiodic {0,1} labelings of the two-dimensional infinite lattice graph. We give X the Bernoulli shift action, and this action induces a graph on X in which each connected component is again a two-dimensional lattice graph. It is folklore that no continuous (indeed, Borel) function provides a two-color

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24

Henry, Michael A. "Various Old and New Results in Classical Arithmetic by Special Functions." Kent State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=kent1524583992694218.

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25

Lam, Wing Chung. "Second moment of the central values of the symmetric square L-functions." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1429139505.

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26

Samson, Duncan Alistair. "An analysis of the influence of question design on pupils' approaches to number pattern generalisation tasks." Thesis, Rhodes University, 2008. http://hdl.handle.net/10962/d1003302.

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This study is based on a qualitative investigation framed within an interpretive paradigm, and aims to investigate the extent to which question design affects the solution strategies adopted by children when solving linear number pattern generalisation tasks presented in pictorial and numeric contexts. The research tool comprised a series of 22 pencil and paper exercises based on linear generalisation tasks set in both numeric and 2-dimensional pictorial contexts. The responses to these linear generalisation questions were classified by means of stage descriptors as well as stage modifiers. Th

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27

Nowland, Kevin John. "Properties of SU(2, 1) Hecke-Maass cusp forms and Eisenstein series." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1543417235410827.

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28

Andrade, Cecília Pereira de 1983. "Sobre novos resultados na teoria das partições." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307512.

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Orientador: José Plínio de Oliveira Santos<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-24T00:20:05Z (GMT). No. of bitstreams: 1 Andrade_CeciliaPereirade_D.pdf: 1476737 bytes, checksum: ad3ad78834fa61c06f515c2172ae896c (MD5) Previous issue date: 2013<br>Resumo: Este trabalho foi baseado em uma nova maneira de representar, combinatoriamente, os coeficientes de várias importantes séries por meio de matrizes de duas linhas. Os resultados que apresentamos neste trabalho foram obtidos p

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29

Carlsson, Simon, and Erik Allgårdh. "Factors Affecting the Number of Trades in ETPs on Nordic Derivatives Exchange." Thesis, KTH, Matematisk statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-275691.

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This thesis examines which factors that affect the number of trades in exchange-traded products (ETPs) on Nordic Derivatives Exchange. Multiple linear regression is used to model the relationship between the number of trades and 65 initially chosen predictor variables. The predictor variables include various indices, commodities, stocks, and volatility measures. Two models are presented, one of which includes a lagged dependent variable. These models explain 89% and 92% of the variance within the data. Foremost, the results confirm previous research advocating the volatility to play a signific

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30

Waller, Bradley A. "Properties of p-adic C^k Distributions." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1385485834.

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31

Letendre, Patrick. "Topics in analytic number theory." Doctoral thesis, Université Laval, 2018. http://hdl.handle.net/20.500.11794/31443.

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Le présent document est un compte-rendu de quatre présentations que j'ai faites au congrès de Théorie des Nombres Québec-Maine entre 2013 et 2016. Au fil des ans, j'ai effectué quelques améliorations et corrections aux documents originaux. Le contenu, l'esprit et l'organisation sont restés essentiellement inchangés. Les quatre sujets sont fondamentalement distincts tout en étant dans un même cercle d'idées. Le premier chapitre traite d'un certain nombre de sujets en relation avec le comportement moyen de certaines fonctions multiplicatives, dans un ensemble bien précis, qui partagent plusieurs

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32

Watt, N. "some problems in analytic number theory." Thesis, Bucks New University, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384667.

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33

Ribeiro, Andreia Cristina. "Aspectos combinatorios de identidades do tipo Rogers-Ramanujan." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307502.

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Orientador: Jose Plinio de Oliveira Santos<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-07T19:25:43Z (GMT). No. of bitstreams: 1 Ribeiro_AndreiaCristina_D.pdf: 576297 bytes, checksum: 445154b7e26e801e909854c976d31c45 (MD5) Previous issue date: 2006<br>Resumo: Neste trabalho são estudadas varias das identidades do tipo Rogers-Ramanujan dadas por Slater. Em 1985, Andrews, introduziram um método geral para se estender para duas variáveis identidades desse tipo de modo a se obter, como

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34

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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35

Brewer, Sky J. "Results in metric and analytic number theory." Thesis, University of York, 2017. http://etheses.whiterose.ac.uk/18381/.

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The following Thesis consists of five chapters. The first three chapters come from Metric Number theory. Chapter 1 discusses algorithms for calculating the continued fraction of algebraic numbers, as well as presenting experimental results on how well algebraic numbers fit well known conjectures on the distribution of their partial quotients. Chapter 2 discusses the Singular and Extremality theories of so called ``well separated Dirichlet type systems''. Chapter 3 presents an effective version of the Khintchine-Groshev theorem for simultaneously small linear forms. The last two chapters are mo

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36

Örström, Simon. "Diophantine approximation and metric number theory." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-452458.

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37

Matomaki, Kaisa Sofia. "Applications of sieve methods in analytic number theory." Thesis, University of London, 2009. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.549585.

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38

Harper, Adam James. "Some topics in analytic and probabilistic number theory." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/265539.

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This dissertation studies four problems in analytic and probabilistic number theory. Two of the problems are about a certain random number theoretic object, namely a random multiplicative function. The other two problems are about smooth numbers (i.e. numbers only having small prime factors), both in their own right and in their application to finding solutions to S-unit equations over the integers. Thus all four problems are concerned, in different ways, with _understanding the multiplicative structure of the integers. More precisely, we will establish that certain sums of a random multiplica

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39

Alghamdi, Maha Mosaad. "ANALYTIC PROOF OF THE PRIME NUMBER THEOREM." Kent State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=kent1550224160190008.

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40

RoÌˆttger, Christian Gottfried Johannes. "Counting problems in algebraic number theory." Thesis, University of East Anglia, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.327407.

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41

Hendi, Yacoub. "On The Prime Number Theorem." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-441288.

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42

Alkauskas, Giedrius. "Several problems from number theory." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2009. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2009~D_20091008_155751-23469.

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Doctoral thesis is devoted to investigation of three problems. The first one deals with the analytic properties and representation in closed or almost closed form of the Stieltjes tranform of the Minkowski question mark function (that is, the generating function of moments, the so called dyadic period function). The main result claims that the dyadic period function can be represented as a convergent series of rational functions with rational coefficients. In the proof the techniques from complex dynamics, analytic theory of continued fractions, the theory of several complex variables are bein

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43

Hoffman, John W. "Some Problems in Additive Number Theory." Kent State University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=kent1408298984.

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44

Burns, Jonathan. "Recursive Methods in Number Theory, Combinatorial Graph Theory, and Probability." Scholar Commons, 2014. https://scholarcommons.usf.edu/etd/5193.

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Recursion is a fundamental tool of mathematics used to define, construct, and analyze mathematical objects. This work employs induction, sieving, inversion, and other recursive methods to solve a variety of problems in the areas of algebraic number theory, topological and combinatorial graph theory, and analytic probability and statistics. A common theme of recursively defined functions, weighted sums, and cross-referencing sequences arises in all three contexts, and supplemented by sieving methods, generating functions, asymptotics, and heuristic algorithms. In the area of number theory, this

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45

Dehkordi, Massoud Hadian. "Asymptotic formulae for some arithmetic functions in number theory." Thesis, Loughborough University, 1998. https://dspace.lboro.ac.uk/2134/12177.

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This thesis gives some asymptotic formulae associated with some non-negative multiplicative functions, and introduce a new method for proof of some classical formulae in number theory using the Laplace transform.

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Cipra, James Arthur. "Waring’s number in finite fields." Diss., Kansas State University, 2010. http://hdl.handle.net/2097/4152.

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Doctor of Philosophy<br>Department of Mathematics<br>Todd E. Cochrane<br>This thesis establishes bounds (primarily upper bounds) on Waring's number in finite fields. Let $p$ be a prime, $q=p^n$, $\mathbb F_q$ be the finite field in $q$ elements, $k$ be a positive integer with $k|(q-1)$ and $t= (q-1)/k$. Let $A_k$ denote the set of $k$-th powers in $\mathbb F_q$ and $A_k' = A_k \cap \mathbb F_p$. Waring's number $\gamma(k,q)$ is the smallest positive integer $s$ such that every element of $\mathbb F_q$ can be expressed as a sum of $s$ $k$-th powers. For prime fields $\mathbb F_p$ we prove that

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47

Kong, Kar-lun, and 江嘉倫. "Some mean value theorems for certain error terms in analytic number theory." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/206432.

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48

Bamunoba, Alex Samuel. "Cyclotomic polynomials (in the parallel worlds of number theory)." Thesis, Stellenbosch : Stellenbosch University, 2011. http://hdl.handle.net/10019.1/17865.

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Thesis (MSc)--Stellenbosch University, 2011.<br>ENGLISH ABSTRACT: It is well known that the ring of integers Z and the ring of polynomials A = Fr[T] over a finite field Fr have many properties in common. It is due to these properties that almost all the famous (multiplicative) number theoretic results over Z have analogues over A. In this thesis, we are devoted to utilising this analogy together with the theory of Carlitz modules. We do this to survey and compare the analogues of cyclotomic polynomials, the size of their coefficients and cyclotomic extensions over the rational function fi

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49

La, Haye Reuben N. "Quantitative Combinatorial Geometry with Applications to Number Theory and Optimization." Thesis, University of California, Davis, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10165904.

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<p> This dissertation contains a variety of results in quantitative combinatorial geometry, as well as applications to optimization and number theory. </p><p> We use Ehrhart theory, the study of the number of lattice points in polytopes, to prove a Rainbow Ramsey analogue of Richard Rado's 1933 result in Ramsey Theory. There were some conjectures as to what this analogue would be; they are disproven by our result. We also prove a few corollaries. </p><p> A portion of this dissertation contains new quantitative variants of classical convexity theorems: whereas the classical theorems have hy

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50

Olofsson, Rikard. "Problems in Number Theory related to Mathematical Physics." Doctoral thesis, Stockholm : Engineering sciences, Kungliga Tekniska högskolan, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-9514.

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