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Analytic Number Theory

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Author(s): Henryk Iwaniec , Emmanuel Kowalski
Series: Colloquium Publications 53
Publisher: American Mathematical Society
Year: 2004

Language: English
Commentary: errata: https://people.math.ethz.ch/~kowalski/corrections-ant.pdf
Pages: 615

Contents
Preface
Introduction
1 Arithmetic functions
2 Elementary theory of prime numbers
3 Characters
4 Summation formulas
5 Classical analytic theory of L-functions
6 Elementary sieve methods
7 Bilinear forms and the large sieve
8 Exponential sums
9 The Dirichlet polynomials
10 Zero-density estimates
11 Sums over finite fields
12 Character sums
13 Sums over primes
14 Holomorphic modular forms
15 Spectral theory of automorphic forms
16 Sums of Kloosterman sums
17 Primes in arithmetic progressions
18 The least prime in an arithmetic progression
19 The Goldbach problem
20 The circle method
21 Equidistribution
22 Imaginary quadratic fields
23 Effective bounds for the class number
24 The critical zeros of the Riemann zeta function
25 The spacing of zeros of the Riemann zeta-function
26 Central values of L-functions
Bibliography
Index