
Analytic Number Theory
American Mathematical Society (Publisher)
Will be published approx. on 30. July 2004
Book
Paperback/Softback
615 pages
978-1-4704-6770-8 (ISBN)
Description
Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results, many of which belong to the mainstream of arithmetic. One of the main attractions of analytic number theory is the vast diversity of concepts and methods it includes. The main goal of the book is to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, its beautiful theorems and powerful techniques.
The book is written with graduate students in mind, and the authors tried to balance between clarity, completeness, and generality. The exercises in each section serve a dual purpose, with some intended to improve the reader's 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 necessary information about them included in two survey chapters.
The book is written with graduate students in mind, and the authors tried to balance between clarity, completeness, and generality. The exercises in each section serve a dual purpose, with some intended to improve the reader's 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 necessary information about them included in two survey chapters.
Reviews / Votes
The book is written in a very lively and nicely readable style ... contains a very well chosen and balanced material. -- EMS Newsletter The authors are active researchers with a lot of experience and deep insight, and their creative attitude makes reading particularly rewarding... It can be warmly recommended toa wide readership ..."" -Zentralblatt MathMore details
Series
Language
English
Place of publication
Providence
United States
Target group
College/higher education
Professional and scholarly
ISBN-13
978-1-4704-6770-8 (9781470467708)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Henryk Iwaniec, Rutgers University, Piscataway, NJ.
Emmanuel Kowalski, Universite Bordeaux I, Talence, France.
Emmanuel Kowalski, Universite Bordeaux I, Talence, France.
Content
Introduction
Arithmetic functions
Elementary theory of prime numbers
Characters
Summation formulas
Classical analytic theory of $L$-functions
Elementary sieve methods
Bilinear forms and the large sieve
Exponential sums
The Dirichlet polynomials
Zero-density estimates
Sums over finite fields
Character sums
Sums over primes
Holomorphic modular forms
Spectral theory of automorphic forms
Sums of Kloosterman sums
Primes in arithmetic progressions
The least prime in an arithmetic progression
The Goldbach problem
The circle method
Equidistribution
Imaginary quadratic fields
Effective bounds for the class number
The critical zeros of the Riemann zeta function
The spacing of zeros of the Riemann zeta-function
Central values of $L$-functions
Bibliography
Index
Arithmetic functions
Elementary theory of prime numbers
Characters
Summation formulas
Classical analytic theory of $L$-functions
Elementary sieve methods
Bilinear forms and the large sieve
Exponential sums
The Dirichlet polynomials
Zero-density estimates
Sums over finite fields
Character sums
Sums over primes
Holomorphic modular forms
Spectral theory of automorphic forms
Sums of Kloosterman sums
Primes in arithmetic progressions
The least prime in an arithmetic progression
The Goldbach problem
The circle method
Equidistribution
Imaginary quadratic fields
Effective bounds for the class number
The critical zeros of the Riemann zeta function
The spacing of zeros of the Riemann zeta-function
Central values of $L$-functions
Bibliography
Index