Softcover ISBN:  9781470467708 
Product Code:  COLL/53.S 
List Price:  $109.00 
MAA Member Price:  $98.10 
AMS Member Price:  $87.20 
Electronic ISBN:  9781470431983 
Product Code:  COLL/53.E 
List Price:  $109.00 
MAA Member Price:  $98.10 
AMS Member Price:  $87.20 

Book DetailsColloquium PublicationsVolume: 53; 2004; 615 ppMSC: Primary 11;
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.ReadershipGraduate students and research mathematicians interested in analytic number theory.

Table of Contents

Chapters

Introduction

Chapter 1. Arithmetic functions

Chapter 2. Elementary theory of prime numbers

Chapter 3. Characters

Chapter 4. Summation formulas

Chapter 5. Classical analytic theory of $L$functions

Chapter 6. Elementary sieve methods

Chapter 7. Bilinear forms and the large sieve

Chapter 8. Exponential sums

Chapter 9. The Dirichlet polynomials

Chapter 10. Zerodensity estimates

Chapter 11. Sums over finite fields

Chapter 12. Character sums

Chapter 13. Sums over primes

Chapter 14. Holomorphic modular forms

Chapter 15. Spectral theory of automorphic forms

Chapter 16. Sums of Kloosterman sums

Chapter 17. Primes in arithmetic progressions

Chapter 18. The least prime in an arithmetic progression

Chapter 19. The Goldbach problem

Chapter 20. The circle method

Chapter 21. Equidistribution

Chapter 22. Imaginary quadratic fields

Chapter 23. Effective bounds for the class number

Chapter 24. The critical zeros of the Riemann zeta function

Chapter 25. The spacing of zeros of the Riemann zetafunction

Chapter 26. Central values of $L$functions


Additional Material

Reviews

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 Math


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 Get Permissions
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.
Graduate students and research mathematicians interested in analytic number theory.

Chapters

Introduction

Chapter 1. Arithmetic functions

Chapter 2. Elementary theory of prime numbers

Chapter 3. Characters

Chapter 4. Summation formulas

Chapter 5. Classical analytic theory of $L$functions

Chapter 6. Elementary sieve methods

Chapter 7. Bilinear forms and the large sieve

Chapter 8. Exponential sums

Chapter 9. The Dirichlet polynomials

Chapter 10. Zerodensity estimates

Chapter 11. Sums over finite fields

Chapter 12. Character sums

Chapter 13. Sums over primes

Chapter 14. Holomorphic modular forms

Chapter 15. Spectral theory of automorphic forms

Chapter 16. Sums of Kloosterman sums

Chapter 17. Primes in arithmetic progressions

Chapter 18. The least prime in an arithmetic progression

Chapter 19. The Goldbach problem

Chapter 20. The circle method

Chapter 21. Equidistribution

Chapter 22. Imaginary quadratic fields

Chapter 23. Effective bounds for the class number

Chapter 24. The critical zeros of the Riemann zeta function

Chapter 25. The spacing of zeros of the Riemann zetafunction

Chapter 26. Central values of $L$functions

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 Math