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Dissertations / Theses on the topic 'Number theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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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

Harbour, Daniel 1975. "Elements of number theory." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/17581.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 2003.<br>Includes bibliographical references (leaves 202-205).<br>The dissertation argues for the necessity of a morphosemantic theory of number, that is, a theory of number serviceable both to semantics and morphology. The basis for this position, and the empirical core of the dissertation, is the relationship between semantically based noun classification and agreement in Kiowa, an indigenous, endangered language of Oklahoma. The central claim is that Universal Grammar provides three number features,

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5

Anderson, Crystal Lynn. "An Introduction to Number Theory Prime Numbers and Their Applications." Digital Commons @ East Tennessee State University, 2006. https://dc.etsu.edu/etd/2222.

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The author has found, during her experience teaching students on the fourth grade level, that some concepts of number theory haven't even been introduced to the students. Some of these concepts include prime and composite numbers and their applications. Through personal research, the author has found that prime numbers are vital to the understanding of the grade level curriculum. Prime numbers are used to aide in determining divisibility, finding greatest common factors, least common multiples, and common denominators. Through experimentation, classroom examples, and homework, the author has i

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6

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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7

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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8

Amirkhanyan, Gagik M. "Problems in combinatorial number theory." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51865.

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The dissertation consists of two parts. The first part is devoted to results in Discrepancy Theory. We consider geometric discrepancy in higher dimensions (d > 2) and obtain estimates in Exponential Orlicz Spaces. We establish a series of dichotomy-type results for the discrepancy function which state that if the L¹ norm of the discrepancy function is too small (smaller than the conjectural bound), then the discrepancy function has to be very large in some other function space.The second part of the thesis is devoted to results in Additive Combinatorics. For a set with small doubling an order-

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9

Rowe, Paul Michael Dominic. "Contributions to metric number theory." Thesis, Royal Holloway, University of London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.408263.

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10

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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11

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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12

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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13

Bulinski, Kamil. "Interactions between Ergodic Theory and Combinatorial Number Theory." Thesis, The University of Sydney, 2017. http://hdl.handle.net/2123/17733.

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The seminal work of Furstenberg on his ergodic proof of Szemerédi’s Theorem gave rise to a very rich connection between Ergodic Theory and Combinatorial Number Theory (Additive Combinatorics). The former is concerned with dynamics on probability spaces, while the latter is concerned with Ramsey theoretic questions about the integers, as well as other groups. This thesis further develops this symbiosis by establishing various combinatorial results via ergodic techniques, and vice versa. Let us now briefly list some examples of such. A shorter ergodic proof of the following theorem of Magyar is

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14

Ho, Kwan-hung, and 何君雄. "On the prime twins conjecture and almost-prime k-tuples." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B29768421.

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15

Chan, Ching-yin, and 陳靖然. "On k-tuples of almost primes." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hdl.handle.net/10722/195967.

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16

Bronder, Justin S. "The AKS Class of Primality Tests: A Proof of Correctness and Parallel Implementation." Fogler Library, University of Maine, 2006. http://www.library.umaine.edu/theses/pdf/BronderJS2006.pdf.

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17

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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18

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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19

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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20

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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21

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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22

Acciaro, Vincenzo Carleton University Dissertation Computer Science. "Local global methods in number theory." Ottawa, 1995.

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23

Shoup, Victor. "Removing randomness from computational number theory." Madison, Wis. : University of Wisconsin-Madison, Computer Sciences Dept, 1989. http://catalog.hathitrust.org/api/volumes/oclc/20839526.html.

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24

Loveless, Andrew David. "Extensions in the theory of Lucas and Lehmer pseudoprimes." Online access for everyone, 2005. http://www.dissertations.wsu.edu/Dissertations/Summer2005/a%5Floveless%5F070705.pdf.

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25

Shahabi, Majid. "The distribution of the classical error terms of prime number theory." Thesis, Lethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Science, c2012, 2012. http://hdl.handle.net/10133/3252.

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26

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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27

at, Gerald Teschl@univie ac. "On the Number of Eigenvalues of Jacobi Operators." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1079.ps.

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28

Schinck, Amelie. "The local-global principle in number theory." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/MQ64047.pdf.

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29

Dyer, A. K. "Applications of sieve methods in number theory." Thesis, Bucks New University, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384646.

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30

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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31

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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32

Griffin, Cornelius John. "Subgroups of infinite groups : interactions between group theory and number theory." Thesis, University of Nottingham, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.252018.

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33

Ki, Haseo Kechris A. S. Kechris A. S. "Topics in descriptive set theory related to number theory and analysis /." Diss., Pasadena, Calif. : California Institute of Technology, 1995. http://resolver.caltech.edu/CaltechETD:etd-10112007-111738.

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34

Hughes, Garry. "Distribution of additive functions in algebraic number fields." Title page, contents and summary only, 1987. http://web4.library.adelaide.edu.au/theses/09SM/09smh893.pdf.

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35

Kong, Yafang, and 孔亚方. "On linear equations in primes and powers of two." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B50533769.

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It is known that the binary Goldbach problem is one of the open problems on linear equations in primes, and it has the Goldbach-Linnik problem, that is, representation of an even integer in the form of two odd primes and powers of two, as its approximate problem. The theme of my research is on linear equations in primes and powers of two. Precisely, there are two cases: one pair of linear equations in primes and powers of two, and one class of pairs of linear equations in primes and powers of two, in this thesis. In 2002, D.R. Heath-Brown and P.C. Puchta obtained that every sufficiently lar

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36

Ketkar, Pallavi S. (Pallavi Subhash). "Primitive Substitutive Numbers are Closed under Rational Multiplication." Thesis, University of North Texas, 1998. https://digital.library.unt.edu/ark:/67531/metadc278637/.

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Lehr (1991) proved that, if M(q, r) denotes the set of real numbers whose expansion in base-r is q-automatic i.e., is recognized by an automaton A = (Aq, Ar, ao, δ, φ) (or is the image under a letter to letter morphism of a fixed point of a substitution of constant length q) then M(q, r) is closed under addition and rational multiplication. Similarly if we let M(r) denote the set of real numbers α whose base-r digit expansion is ultimately primitive substitutive, i.e., contains a tail which is the image (under a letter to letter morphism) of a fixed point of a primitive substitution then in an

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37

Trad, Mohamad. "The proof of Fermat's last theorem." CSUSB ScholarWorks, 2000. https://scholarworks.lib.csusb.edu/etd-project/1690.

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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

Tringali, Salvatore. "Some questions in combinatorial and elementary number theory." Phd thesis, Université Jean Monnet - Saint-Etienne, 2013. http://tel.archives-ouvertes.fr/tel-01060871.

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This thesis is divided into two parts. Part I is about additive combinatorics. Part II deals with questions in elementary number theory. In Chapter 1, we generalize the Davenport transform to prove that if si S\mathbb A=(A, +)S is acancellative semigroup (either abelian or not) and SX, YS are non-empty subsets of SAS such that the subsemigroup generated by SYS is abelian, then SS|X+Y|\gc\min(\gamma(Y, |X|+|Y|-I)SS, where for SZ\subsetcq AS we let S\gamma(Z):=\sup_{z_0\in Z^\times}\in f_(z_0\nc z\inZ) (vm ord)(z-z_0)S. This implies an extension of Chowla's and Pillai's theorems for cyclic group

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40

Thorn, Rebecca Emily. "Metric number theory : the good and the bad." Thesis, Queen Mary, University of London, 2005. http://qmro.qmul.ac.uk/xmlui/handle/123456789/28568.

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Each aspect of this thesis is motivated by the recent paper of Beresnevich, Dickinson and Velani (BDV03]. Let 'ljJ be a real, positive, decreasing function i.e. an approximation function. Their paper considers a general lim sup set A( 'ljJ), within a compact metric measure space (0, d, m), consisting of points that sit in infinitely many balls each centred at an element ROt of a countable set and of radius 'I/J(130) where 130 is a 'weight' assigned to each ROt. The classical set of 'I/J-well approximable numbers is the basic example. For the set A('ljJ) , [BDV03] achieves m-measure and Hausdor

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41

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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42

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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43

Swanson, Colleen M. "Algebraic number fields and codes /." Connect to online version, 2006. http://ada.mtholyoke.edu/setr/websrc/pdfs/www/2006/172.pdf.

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44

Polzin, Marc. "Prolongement de la valeur absolue de Gauss et problème de Skolem." Bordeaux 1, 1987. http://www.theses.fr/1987BOR10539.

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Dans cette these, nous nous interessons au probleme suivant : soit k un corps value ultrametrique, non necessairement complet, l un corps de fonctions d'une variable sur k, w un ensemble fini de valeurs absolues sur l qui prolongent celle de k et telles que le corps residuel de l soit un corps de fonctions d'une variable sur le corps residuel de k. Existe-t-il t dans l, transcendant sur k, tel que w soit exactement l'ensemble des prolongements a l de la valeur absolue de gauss sur k(t) associee a t. Nous donnons, dans la partie 2, une condition equivalente en termes geometriques en utilisant l

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45

Landreau, Bernard. "Majorations de fonctions arithmétiques en moyenne sur des ensembles de faible densité." Bordeaux 1, 1987. http://www.theses.fr/1987BOR10629.

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Le but de cette these est d'etablir des majorations de valeurs de fonctions arithmetiques f, en moyenne sur des ensembles d'entiers a de faible densite exponentielle. En suivant des idees d'erdoes et nicolas, on commence par traiter le cas ou les ensembles a n'ont aucune structure particuliere. Il est alors possible de majorer la valeur moyenne de f sur a par une puissance du maximum de f sur a, avec un exposant inferieur a 1, d'autant plus proche de zero que l'ensemble a est riche. La partie principale du travail consiste a obtenir des majorations de la valeur f(n) par une somme de valeurs f(

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46

Louboutin, Stéphane. "Arithmetique des corps quadratiques reels et fractions continues." Paris 7, 1987. http://www.theses.fr/1987PA077077.

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En appliquant la theorie des fractions continues a l'etude de l'arithmetique des corps quadratiques reels, nous pouvons repondre aux questions suivantes: 1) nous donnons deux criteres de principalite des corps quadratiques reels, le premier ne faisant intervenir que le caractere du corps et des invariants lies aux developpements en fractions continues, le second etant un equivalent reel du theoreme de frobenius-rabinovitch (qui caracterisait les corps quadratiques imaginaires principaux) et faisant intervenir ces memes invariants. 2) nous determinons (explicitement sous l'hypothese de riemann)

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47

Emsalem, Michel. "I : Deux problèmes d'analyse réelle et p-adique. II: Autour de la conjecture de Leopoldt : Un point de vue transcendant." Paris 6, 1987. http://www.theses.fr/1987PA066069.

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Le present recueil de travaux comporte deux parties. La premiere traite deux problemes d'analyse reelle et p-adique. L'un concerne les fonctions moyenne periodiques et les fonctions presque periodiques dont le spectre possede une certaine propriete arithmetique, l'autre porte sur l'approximation ponderee de fonctions sur un corps de nombres p-adiques. La seconde partie a pour theme l'application de theoremes de transcendance a des situations de theorie des nombres. Les ingredients transcendants sont d'un cote le theoreme de baker-brumer sur l'independance lineaire sur q de logarithmes p-adique

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48

Langevin, Michel. "Methodes transcendantes en theorie des nombres." Paris 6, 1987. http://www.theses.fr/1987PA066178.

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Par une utilisation conjointe de techniques de transcendance ou elementaires, on minore soit le plus grand facteur premier, soit la partie sans facteur carre, soit encore le nombre de diviseurs premiers de produits d'entiers en progression arithmetique ou de termes de meme nature. On aborde egalement par ces procedes le probleme d'erdoes-woods, la conjecture de grimm. . . Dans une seconde partie, on emploie le schema des demonstrations de transcendance pour etudier des problemes de theorie des nombres ou d'analyse lies a la repartition des zeros des polynomes : probleme de lehmer, probleme de

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49

Balazard, Michel. "Sur la repartition des valeurs de certaines fonctions arithmetiques additives." Limoges, 1987. http://www.theses.fr/1987LIMO0014.

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Ce travail concerne la distribution des valeurs de fonctions arithmétiques comptant, de diverses facons, le nombre de facteurs premiers d'un entier. Lorsqu'on se restreint aux facteurs premiers appartenant a un ensemble E, on obtient un encadrement uniforme des lois locales. Cet encadrement est remplacé par une formule asymptotique si E est l'ensemble de tous les nombres premiers ou si l'on limite a un certain domaine le parametre des lois locales. On aborde aussi l'étude de la distribution conjointe de deux fonctions additives, obtenant ainsi des formules a terme principal discontinu pour les

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50

Azzouza, Nour-Eddine. "Majorations effectives du nombre d'entiers inferieurs a x, et ayant exactement k facteurs premiers." Limoges, 1988. http://www.theses.fr/1988LIMO0032.

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Soit n(x,k), le cardinal de l'ensemble des entiers inferieurs a x, et ayant une quantite fixee k, de facteurs premiers. On etudie le comportement de cette quantite pour en obtenir une formule asymptotique uniforme pour k dans un intervalle donne. Il est interessant d'etablir des majorations effectives de n(x,k) valable pour tout k entier. Le resultat depend de majorations explicites de sommes de fonctions arithmetiques

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