**Colloquium Publications**

Volume: 53;
2004;
615 pp;
Hardcover

MSC: Primary 11;

Print ISBN: 978-0-8218-3633-0

Product Code: COLL/53

List Price: $109.00

Individual Member Price: $87.20

**Electronic ISBN: 978-1-4704-3198-3
Product Code: COLL/53.E**

List Price: $109.00

Individual Member Price: $87.20

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#### Supplemental Materials

# Analytic Number Theory

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*Henryk Iwaniec; Emmanuel Kowalski*

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.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## Analytic Number Theory

- Cover Cover11
- Title page iii4
- Contents v6
- Preface xi12
- Introduction 114
- Arithmetic functions 922
- Elementary theory of prime numbers 3144
- Characters 4356
- Summation formulas 6578
- Classical analytic theory of 𝐿-functions 93106
- Elementary sieve methods 153166
- Bilinear forms and the large sieve 169182
- Exponential sums 197210
- The Dirichlet polynomials 229242
- Zero-density estimates 249262
- Sums over finite fields 269282
- Character sums 317330
- Sums over primes 337350
- Holomorphic modular forms 353366
- Spectral theory of automorphic forms 383396
- Sums of Kloosterman sums 403416
- Primes in arithmetic progressions 419432
- The least prime in an arithmetic progression 427440
- The Goldbach problem 443456
- The circle method 449462
- Equidistribution 487500
- Imaginary quadratic fields 503516
- Effective bounds for the class number 529542
- The critical zeros of the Riemann zeta function 547560
- The spacing of zeros of the Riemann zeta-function 563576
- Central values of 𝐿-functions 577590
- Bibliography 599612
- Index 611624
- Back Cover Back Cover1632