Zeta And L Functions In Number Theory And Combinatorics

Author : Wen-Ching Winnie Li
Publisher : Unknown
Page : 128 pages
File Size : 49,8 Mb
Release : 2019
Category : Combinatorial number theory
ISBN : 1470451921

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Zeta and L-functions in Number Theory and Combinatorics by Wen-Ching Winnie Li Pdf

Zeta and L-functions play a central role in number theory. They provide important information of arithmetic nature. This book, which grew out of the author's teaching over several years, explores the interaction between number theory and combinatorics using zeta and L-functions as a central theme. It provides a systematic and comprehensive account of these functions in a combinatorial setting and establishes, among other things, the combinatorial counterparts of celebrated results in number theory, such as the prime number theorem and the Chebotarev density theorem. The spectral theory for fin.

Author : Wen-Ching Winnie Li
Publisher : American Mathematical Soc.
Page : 95 pages
File Size : 46,8 Mb
Release : 2019-03-01
Category : Combinatorial number theory
ISBN : 9781470449001

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Zeta and L -functions in Number Theory and Combinatorics by Wen-Ching Winnie Li Pdf

Zeta and L-functions play a central role in number theory. They provide important information of arithmetic nature. This book, which grew out of the author's teaching over several years, explores the interaction between number theory and combinatorics using zeta and L-functions as a central theme. It provides a systematic and comprehensive account of these functions in a combinatorial setting and establishes, among other things, the combinatorial counterparts of celebrated results in number theory, such as the prime number theorem and the Chebotarev density theorem. The spectral theory for finite graphs and higher dimensional complexes is studied. Of special interest in theory and applications are the spectrally extremal objects, called Ramanujan graphs and Ramanujan complexes, which can be characterized by their associated zeta functions satisfying the Riemann Hypothesis. Explicit constructions of these extremal combinatorial objects, using number-theoretic and combinatorial means, are presented. Research on zeta and L-functions for complexes other than graphs emerged only in recent years. This is the first book for graduate students and researchers offering deep insight into this fascinating and fast developing area.

Author : Bruno Kahn
Publisher : Cambridge University Press
Page : 217 pages
File Size : 42,6 Mb
Release : 2020-05-07
Category : Mathematics
ISBN : 9781108703390

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Zeta and L-Functions of Varieties and Motives by Bruno Kahn Pdf

Discover how zeta and L-functions have shaped the development of major parts of mathematics over the past two centuries.

Author : Carlos J. Moreno
Publisher : American Mathematical Soc.
Page : 313 pages
File Size : 44,6 Mb
Release : 2005
Category : Algebraic number theory
ISBN : 9780821842669

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Advanced Analytic Number Theory: L-Functions by Carlos J. Moreno Pdf

Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois representations. This book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and non-vanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of Artin-Hecke and automorphic L-functions is also given. The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of L-functions and their applications in number theory and in the theory of automorphic representations. The requirements for a profitable study of this monograph are a knowledge of basic number theory and the rudiments of abstract harmonic analysis on locally compact abelian groups.

Author : Minking Eie
Publisher : World Scientific
Page : 313 pages
File Size : 54,5 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814472647

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The Theory of Multiple Zeta Values with Applications in Combinatorics by Minking Eie Pdf

This is the first book on the theory of multiple zeta values since its birth around 1994. Readers will find that the shuffle products of multiple zeta values are applied to complicated counting problems in combinatorics, producing numerous interesting identities that are ready to be used. This will provide a powerful tool to deal with problems in multiple zeta values, both in evaluations and shuffle relations. The volume will benefit graduate students doing research in number theory.

Author : Anatoly A. Karatsuba,S. M. Voronin
Publisher : Walter de Gruyter
Page : 409 pages
File Size : 46,5 Mb
Release : 2011-05-03
Category : Mathematics
ISBN : 9783110886146

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The Riemann Zeta-Function by Anatoly A. Karatsuba,S. M. Voronin Pdf

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Author : Gradimir V. Milovanović,Michael Th. Rassias
Publisher : Springer
Page : 873 pages
File Size : 55,7 Mb
Release : 2014-07-08
Category : Mathematics
ISBN : 9781493902583

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Analytic Number Theory, Approximation Theory, and Special Functions by Gradimir V. Milovanović,Michael Th. Rassias Pdf

This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.

Author : Marius Overholt
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 43,5 Mb
Release : 2014-12-30
Category : Mathematics
ISBN : 9781470417062

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A Course in Analytic Number Theory by Marius Overholt Pdf

This book is an introduction to analytic number theory suitable for beginning graduate students. It covers everything one expects in a first course in this field, such as growth of arithmetic functions, existence of primes in arithmetic progressions, and the Prime Number Theorem. But it also covers more challenging topics that might be used in a second course, such as the Siegel-Walfisz theorem, functional equations of L-functions, and the explicit formula of von Mangoldt. For students with an interest in Diophantine analysis, there is a chapter on the Circle Method and Waring's Problem. Those with an interest in algebraic number theory may find the chapter on the analytic theory of number fields of interest, with proofs of the Dirichlet unit theorem, the analytic class number formula, the functional equation of the Dedekind zeta function, and the Prime Ideal Theorem. The exposition is both clear and precise, reflecting careful attention to the needs of the reader. The text includes extensive historical notes, which occur at the ends of the chapters. The exercises range from introductory problems and standard problems in analytic number theory to interesting original problems that will challenge the reader. The author has made an effort to provide clear explanations for the techniques of analysis used. No background in analysis beyond rigorous calculus and a first course in complex function theory is assumed.

Author : Jürgen Sander,Jörn Steuding,Rasa Steuding
Publisher : Springer
Page : 552 pages
File Size : 47,5 Mb
Release : 2016-12-29
Category : Mathematics
ISBN : 9783319282039

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From Arithmetic to Zeta-Functions by Jürgen Sander,Jörn Steuding,Rasa Steuding Pdf

This book collects more than thirty contributions in memory of Wolfgang Schwarz, most of which were presented at the seventh International Conference on Elementary and Analytic Number Theory (ELAZ), held July 2014 in Hildesheim, Germany. Ranging from the theory of arithmetical functions to diophantine problems, to analytic aspects of zeta-functions, the various research and survey articles cover the broad interests of the well-known number theorist and cherished colleague Wolfgang Schwarz (1934-2013), who contributed over one hundred articles on number theory, its history and related fields. Readers interested in elementary or analytic number theory and related fields will certainly find many fascinating topical results among the contributions from both respected mathematicians and up-and-coming young researchers. In addition, some biographical articles highlight the life and mathematical works of Wolfgang Schwarz.

Author : J. B. Friedlander,D. R. Heath-Brown,Henryk Iwaniec,J. Kaczorowski
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 41,6 Mb
Release : 2006
Category : Electronic
ISBN : 9783540363637

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Analytic Number Theory by J. B. Friedlander,D. R. Heath-Brown,Henryk Iwaniec,J. Kaczorowski Pdf

Author : Kağan Kurşungöz,Ayberk Zeytin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 129 pages
File Size : 51,9 Mb
Release : 2021-11-08
Category : Mathematics
ISBN : 9783110761191

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Number Theory by Kağan Kurşungöz,Ayberk Zeytin Pdf

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Author : Robert Spira
Publisher : Unknown
Page : 424 pages
File Size : 52,9 Mb
Release : 1999
Category : Functions, Zeta
ISBN : CORNELL:31924086163080

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History of Zeta Functions by Robert Spira Pdf

Author : Marcus du Sautoy,Luke Woodward
Publisher : Springer Science & Business Media
Page : 217 pages
File Size : 49,6 Mb
Release : 2008
Category : Mathematics
ISBN : 9783540747017

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Zeta Functions of Groups and Rings by Marcus du Sautoy,Luke Woodward Pdf

Zeta functions have been a powerful tool in mathematics over the last two centuries. This book considers a new class of non-commutative zeta functions which encode the structure of the subgroup lattice in infinite groups. The book explores the analytic behaviour of these functions together with an investigation of functional equations. Many important examples of zeta functions are calculated and recorded providing an important data base of explicit examples and methods for calculation.

Author : Daniel Bump,Solomon Friedberg,Dorian Goldfeld
Publisher : Springer
Page : 361 pages
File Size : 50,8 Mb
Release : 2012-07-09
Category : Mathematics
ISBN : 9780817683344

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Multiple Dirichlet Series, L-functions and Automorphic Forms by Daniel Bump,Solomon Friedberg,Dorian Goldfeld Pdf

Multiple Dirichlet Series, L-functions and Automorphic Forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic forms that exhibits surprising and deep connections to crystal graphs and mathematical physics. As such, it represents a new way in which areas including number theory, combinatorics, statistical mechanics, and quantum groups are seen to fit together. The volume also includes papers on automorphic forms and L-functions and related number-theoretic topics. This volume will be a valuable resource for graduate students and researchers in number theory, combinatorics, representation theory, mathematical physics, and special functions. Contributors: J. Beineke, B. Brubaker, D. Bump, G. Chinta, G. Cornelissen, C.A. Diaconu, S. Frechette, S. Friedberg, P. Garrett, D. Goldfeld, P.E. Gunnells, B. Heim, J. Hundley, D. Ivanov, Y. Komori, A.V. Kontorovich, O. Lorscheid, K. Matsumoto, P.J. McNamara, S.J. Patterson, M. Suzuki, H. Tsumura.

Author : Tsuneo Arakawa,Tomoyoshi Ibukiyama,Masanobu Kaneko
Publisher : Springer
Page : 278 pages
File Size : 41,5 Mb
Release : 2014-07-11
Category : Mathematics
ISBN : 9784431549192

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Bernoulli Numbers and Zeta Functions by Tsuneo Arakawa,Tomoyoshi Ibukiyama,Masanobu Kaneko Pdf

Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausen–von Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of p-adic measures; the Euler–Maclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of exponential sums expressed by generalized Bernoulli numbers; the relation between ideal classes of orders of quadratic fields and equivalence classes of binary quadratic forms; class number formula for positive definite binary quadratic forms; congruences between some class numbers and Bernoulli numbers; simple zeta functions of prehomogeneous vector spaces; Hurwitz numbers; Barnes multiple zeta functions and their special values; the functional equation of the doub le zeta functions; and poly-Bernoulli numbers. An appendix by Don Zagier on curious and exotic identities for Bernoulli numbers is also supplied. This book will be enjoyable both for amateurs and for professional researchers. Because the logical relations between the chapters are loosely connected, readers can start with any chapter depending on their interests. The expositions of the topics are not always typical, and some parts are completely new.