解析数论的一大特点是能够利用多种工具获得所需的结果。这个理论的一个主要迷人之处是它的概念和方法的极大多样化。本书的主要目的是呈现这个理论在经典和现代两个方向上的适用范围，并展示其丰富内涵和前景、漂亮的定理以及强有力的技术。
为了让研究生更好地阅读，作者很好地兼顾了叙述的清晰性、内容的完整性及知识的广度。每一节的习题都含有双重目的，一些题目用作增进读者对主题的理解，另外一些则提供了更多的信息。本书的主要内容所要求的预备知识仅限于微积分、复分析、积分学和傅里叶级数与傅里叶积分。后面一些章节中的自守形式很重要，学习它们所必需的大部分信息包含在两个概述章中。
本书适合于对解析数论感兴趣的研究生阅读，也可供相关研究人员参考。

Preface
Introduction
Chapter 1. Arithmetic Functions
1.1. Notation and definitions
1.2. Generating series
1.3. Dirichlet convolution
1.4. Examples
1.5. Arithmetic functions on average
1.6. Sums of multiplicative functions
1.7. Distribution of additive functions
Chapter 2. Elementary Theory of Prime Numbers
2.1. The Prime Number Theorem
2.2. Tchebyshev method
2.3. Primes in arithmetic progressions
2.4. Reflections on elementary proofs of the Prime Number Theorem
Chapter 3. Characters
3.1. Introduction
3.2. Dirichlet characters
3.3. Primitive characters
3.4. Gauss sums
3.5. Real characters
3.6. The quartic residue symbol
3.7. The Jacobi-Dirichlet and the Jacobi-Kubota symbols
3.8. Hecke characters
Chapter 4. Summation Formulas
$4.1. Introduction
4.2. The Euler-Maclaurin formula
4.3. The Poisson summation formula
4.4. Summation formulas for the ball
4.5. Summation formulas for the hyperbola
4.6. Functional equations of Dirichlet L-functions
4.A. Appendix: Fourier integrals and series
Chapter 5. Classical Analytic Theory of L-functions
5.1. Definitions and preliminaries
5.2. Approximations to L-functions
5.3. Counting zeros of L-functions
5.4. The zero-free region
5.5. Explicit formula
5.6. The prime number theorem
5.7. The Grand Riemann Hypothesis
5.8. Simple consequences of GRH
5.9. The Riemann zeta function and Dirichlet L-functions
5.10. L-functions of number fields
5.11. Classical automorphic L-functions
5.12. General automorphic L-functions
5.13. Artin L-functions
5.14. L-functions of varieties
5.A. Appendix: complex analysis
Chapter 6. Elementary Sieve Methods
6.1. Sieve problems
6.2. Exclusion-inclusion scheme
6.3. Estimations of V+(z), V-(z)
6.4. Fundamental Lemma of sieve theory
6.5. The A2-Sieve
6.6. Estimate for the main term of the A2-sieve
6.7. Estimates for the remainder term in the A2-sieve
6.8. Selected applications of A2-sieve
Chapter 7. Bilinear Forms and the Large Sieve
7.1. General principles of estimating double sums
7.2. Bilinear forms with exponentials
7.3. Introduction to the large sieve
7.4. Additive large sieve inequalities
7.5. Multiplicative large sieve inequality
7.4. Applications of the large sieve to sieving problems
7.6. Panorama of the large sieve inequalities
7.7. Large sieve inequalities for cusp forms
7.8. Orthogonality of elliptic curves
7.9. Power moments of L-functions
Chapter 8. Exponential Sums
8.1. Introduction
8.2. Weyl's method
8.3. Van der Corput method
8.4. Discussion of exponent pairs
8.5. Vinogradov's method
Chapter 9. The Dirichlet Polynomials
9.1. Introduction
9.2. The integral mean-value estimates
9.3. The discrete mean-value estimates
9.4. Large values of Dirichlet polynomials
9.5. Dirichlet polynomials with characters
9.6. The reflection method
9.7. Large values of D(s, X)
Chapter 10. Zero Density Estimates
10.1. Introduction
10.2. Zero-detecting polynomials
10.3. Breaking the zero-density conjecture
10.4. Grand zero-density theorem
10.5. The gaps between primes
Chapter 11. Sums over Finite Fields
11.1. Introduction
11.2. Finite fields
11.3. Exponential sums
11.4. The Hasse-Davenport relation
11.5. The zeta function for Kloosterman sums
11.6. Stepanov's method for hyperelliptic curves
11.7. Proof of Weil's bound for Kloosterman sums
11.8. The Riemann Hypothesis for elliptic curves over finite fields
11.9. Geometry of elliptic curves
11.10. The local zeta function of elliptic curves
11.11. Survey of further results: a cohomological primer
11.12. Comments
Chapter 12. Character Sums
12.1. Introduction
12.2. Completing methods
12.3. Complete character sums
12.4. Short character sums
12.5. Very short character sums to highly composite modulus
12.6. Characters to powerful modulus