解析数论问题集（英文版）
作者： 默尔蒂
出版时间：2014年5月
出版社：哈尔滨工业大学出版社
- 哈尔滨工业大学出版社
- 9787560346885
- 1-1
- 181276
- 0042166158-8
- 2014年5月
- 理学
- 数学
- O156.4
- 数学类
- 研究生、本科
Preface to the Second Edition
Acknowledgments for the Second Edition
Preface to the First Edition
Acknowledgments for the First Edition
I Problems
1 Arithmetic Functions
1.1 The Mobius Inversion Formula and Applications
1.2 Formal Dirichlet Series
1.3 Orders of Some Arithmetical Functions
1.4 Average Orders of Arithmetical Functions
1.5 Supplementary Problems
2 Primes in Arithmetic Progressions
2.1 Summation Techniques
2.2 Characters mod q
2.3 Dirichlet's Theorem
2.4 Dirichlet's Hyperbola Method
2.5 Supplementary Problems
3 The Prime Number Theorem
3.1 Chebyshev's Theorem
3.2 Nonvanishing of Dirichlet Series on Re(s) = 1
3.3 The Ikehara - Wiener Theorem
3.4 Supplementary Problems
4 The Method of Contour Integration
4.1 Some Basic Integrals
4.2 The Prime Number Theorem
4.3 Further Examples
4.4 Supplementary Problems
5 Functional Equations
5.1 Poisson's Summation Formula
5.2 The Riemann Zeta Function
5.3 Gauss Sums
5.4 Dirichlet L-functions
5.5 Supplementary Problems
6 Hadamard Products
6.1 Jensen's Theorem
6.2 Entire Functions of Order I
6.3 The Gamma Function
6.4 Infinite Products for ξ(s) and ξ(s, X)
6.5 Zero-Free Regions for □(s) and G(s, X)
6.6 Supplementary Problems
7 Explicit Formulas
7.1 Counting Zeros
7.2 Explicit Formula for ψ(x)
7.3 Weil's Explicit Formula
7.4 Supplementary Problems
8 The Selberg Class
8.1 The Phragmen- Lindelof Theorem
8.2 Basic Properties
8.3 Selberg's Conjectures
8.4 Supplementary Problems
9 Sieve Methods
9.1 The Sieve of Eratosthenes
9.2 Brun's Elementary Sieve
9.3 Selberg's Sieve
9.4 Supplementary Problems
10 p-adic Methods
10.10strowski's Theorem
10.2 Hensel's Lemma
10.3 p-adic Interpolation
10.4 The p-adic Zeta-Function
10.5 Supplementary Problems
11 Equidistribution
11.1 Uniform distribution modulo 1
11.2 Normal numbers
11.3 Asymptotic distribution functions mod 1
11.4 Discrepancy
11.5 Equidistribution and L-functions
11.6 Supplementary Problems
II Solutions
1 Arithmetic Functions
1.1 The Mobius Inversion Formula and Applications
1.2 Formal Dirichlet Series
1.3 Orders of Some Arithmetical Functions
1.4 Average Orders of Arithmetical Functions
1.5 Supplementary Problems
2 Primes in Arithmetic Progressions
2.1 Characters mod q
2.2 Dirichlet's Theorem
2.3 Dirichlet's Hyperbola Method
2.4 Supplementary Problems
3 The Prime Number Theorem
3.1 Chebyshev's Theorem
3.2 Nonvanishing of Dirichlet Series on Re(s) = 1
3.3 The Ikehara - Wiener Theorem
3.4 Supplementary Problems
4 The Method of Contour Integration
4.1 Some Basic Integrals
4.2 The Prime Number Theorem
4.3 Further Examples
4.4 Supplementary Problems
5 Functional Equations
5.1 Poisson's Summation Formula
5.2 The Riemann Zeta Function
5.3 Gauss Sums
5.4 Dirichlet L-functions
5.5 Supplementary Problems
6 Hadamard Products
6.1 Jensen's theorem
6.2 The Gamma Function
6.3 Infinite Products for ξ(s) and ξ(s, X)
6.4 Zero-Free Regions for □(s) and L(s, X)
6.5 Supplementary Problems
7 Explicit Formulas
7.1 Counting Zeros
7.2 Explicit Formula for ψ(x)
7.3 Supplementary Problems
8 The Selberg Class
8.1 The Phragmen - Lindelof Theorem
8.2 Basic Properties
8.3 Selberg's Conjectures
8.4 Supplementary Problems
9 Sieve Methods
9.1 The Sieve of Eratosthenes
9.2 Brun's Elementary Sieve
9.3 Selberg's Sieve
9.4 Supplementary Problems
10 p-adic Methods
10.10strowski's Theorem
10.2 Hensel's Lemma
10.3 p-adic Interpolation
10.4 The p-adic □-Function
10.5 Supplementary Problems
11 Equidistribution
11.1 Uniform distribution modulo I
11.2 Normal numbers
11.3 Asymptotic distribution functions mod 1
11.4 Discrepancy
11.5 Equidistribution and L-functio
