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Advanced Analytic Number Theory L Functions

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Advanced Analytic Number Theory L Functions

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Author : Carlos J. Moreno
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Advanced Analytic Number Theory L Functions written by Carlos J. Moreno and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Algebraic number theory categories.

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.

Analytic Number Theory

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Author : J. B. Friedlander
language : en
Publisher: Springer
Release Date : 2006-11-10

Analytic Number Theory written by J. B. Friedlander and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-10 with Mathematics categories.

The four papers collected in this book discuss advanced results in analytic number theory, including recent achievements of sieve theory leading to asymptotic formulae for the number of primes represented by suitable polynomials; counting integer solutions to Diophantine equations, using results from algebraic geometry and the geometry of numbers; the theory of Siegel’s zeros and of exceptional characters of L-functions; and an up-to-date survey of the axiomatic theory of L-functions introduced by Selberg.

Analytic Number Theory

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Author : J. B. Friedlander
language : en
Publisher: Springer
Release Date : 2006-09-15

A Course In Analytic Number Theory

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Author : Marius Overholt
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-30

A Course In Analytic Number Theory written by Marius Overholt and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-30 with Mathematics categories.

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.

Topics In Analytic Number Theory

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Author : Serge Lang
language : en
Publisher:
Release Date : 1961

Topics In Analytic Number Theory written by Serge Lang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Functional analysis categories.

Introduction To Analytic Number Theory

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Author : A. G. Postnikov
language : en
Publisher: American Mathematical Soc.
Release Date : 1988-12-31

Introduction To Analytic Number Theory written by A. G. Postnikov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-12-31 with Mathematics categories.

Aimed at a level between textbooks and the latest research monographs, this book is directed at researchers, teachers, and graduate students interested in number theory and its connections with other branches of science. Choosing to emphasize topics not sufficiently covered in the literature, the author has attempted to give as broad a picture as possible of the problems of analytic number theory.

Complex Analysis In Number Theory

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Author : Anatoly A. Karatsuba
language : en
Publisher: CRC Press
Release Date : 1994-11-22

Complex Analysis In Number Theory written by Anatoly A. Karatsuba and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-11-22 with Mathematics categories.

This book examines the application of complex analysis methods to the theory of prime numbers. In an easy to understand manner, a connection is established between arithmetic problems and those of zero distribution for special functions. Main achievements in this field of mathematics are described. Indicated is a connection between the famous Riemann zeta-function and the structure of the universe, information theory, and quantum mechanics. The theory of Riemann zeta-function and, specifically, distribution of its zeros are presented in a concise and comprehensive way. The full proofs of some modern theorems are given. Significant methods of the analysis are also demonstrated as applied to fundamental problems of number theory.

Analytic Number Theory For Beginners

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Author : Prapanpong Pongsriiam
language : en
Publisher: American Mathematical Society
Release Date : 2023-06-02

Analytic Number Theory For Beginners written by Prapanpong Pongsriiam and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-02 with Mathematics categories.

This new edition of Analytic Number Theory for Beginners presents a friendly introduction to analytic number theory for both advanced undergraduate and beginning graduate students, and offers a comfortable transition between the two levels. The text starts with a review of elementary number theory and continues on to present less commonly covered topics such as multiplicative functions, the floor function, the use of big $O$, little $o$, and Vinogradov notation, as well as summation formulas. Standard advanced topics follow, such as the Dirichlet $L$-function, Dirichlet's Theorem for primes in arithmetic progressions, the Riemann Zeta function, the Prime Number Theorem, and, new in this second edition, sieve methods and additive number theory. The book is self-contained and easy to follow. Each chapter provides examples and exercises of varying difficulty and ends with a section of notes which include a chapter summary, open questions, historical background, and resources for further study. Since many topics in this book are not typically covered at such an accessible level, Analytic Number Theory for Beginners is likely to fill an important niche in today's selection of titles in this field.

Steps Into Analytic Number Theory

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Author : Paul Pollack
language : en
Publisher: Springer Nature
Release Date : 2021-02-08

Steps Into Analytic Number Theory written by Paul Pollack and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-08 with Mathematics categories.

This problem book gathers together 15 problem sets on analytic number theory that can be profitably approached by anyone from advanced high school students to those pursuing graduate studies. It emerged from a 5-week course taught by the first author as part of the 2019 Ross/Asia Mathematics Program held from July 7 to August 9 in Zhenjiang, China. While it is recommended that the reader has a solid background in mathematical problem solving (as from training for mathematical contests), no possession of advanced subject-matter knowledge is assumed. Most of the solutions require nothing more than elementary number theory and a good grasp of calculus. Problems touch at key topics like the value-distribution of arithmetic functions, the distribution of prime numbers, the distribution of squares and nonsquares modulo a prime number, Dirichlet's theorem on primes in arithmetic progressions, and more. This book is suitable for any student with a special interest in developing problem-solving skills in analytic number theory. It will be an invaluable aid to lecturers and students as a supplementary text for introductory Analytic Number Theory courses at both the undergraduate and graduate level.

Analytic Number Theory

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Author : Henryk Iwaniec
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Analytic Number Theory written by Henryk Iwaniec and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results. One of the primary attractions of this theory is its vast diversity of concepts and methods. The main goals of this book are to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, beautiful theorems, and powerful techniques. The book is written with graduate students in mind, and the authors nicely balance clarity, completeness, and generality. The exercises in each section serve dual purposes, some intended to improve readers' understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much of the necessary information about them included in two survey chapters.

Advanced Analytic Number Theory L Functions

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