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Analytic Number Theory
 
Henryk Iwaniec Rutgers University, Piscataway, NJ
Emmanuel Kowalski Université Bordeaux I, Talence, France
Front Cover for Analytic Number Theory
Available Formats:
Softcover ISBN: 978-1-4704-6770-8
Product Code: COLL/53.S
List Price: $109.00
MAA Member Price: $98.10
AMS Member Price: $87.20
Electronic ISBN: 978-1-4704-3198-3
Product Code: COLL/53.E
List Price: $109.00
MAA Member Price: $98.10
AMS Member Price: $87.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $163.50
MAA Member Price: $147.15
AMS Member Price: $130.80
Front Cover for Analytic Number Theory
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  • Front Cover for Analytic Number Theory
  • Back Cover for Analytic Number Theory
Analytic Number Theory
Henryk Iwaniec Rutgers University, Piscataway, NJ
Emmanuel Kowalski Université Bordeaux I, Talence, France
Available Formats:
Softcover ISBN:  978-1-4704-6770-8
Product Code:  COLL/53.S
List Price: $109.00
MAA Member Price: $98.10
AMS Member Price: $87.20
Electronic ISBN:  978-1-4704-3198-3
Product Code:  COLL/53.E
List Price: $109.00
MAA Member Price: $98.10
AMS Member Price: $87.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $163.50
MAA Member Price: $147.15
AMS Member Price: $130.80
  • Book Details
     
     
    Colloquium Publications
    Volume: 532004; 615 pp
    MSC: 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.

    Readership

    Graduate 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. Zero-density 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 zeta-function
    • 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
  • Request Review Copy
  • Get Permissions
Volume: 532004; 615 pp
MSC: 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.

Readership

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. Zero-density 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 zeta-function
  • 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
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