解析数论焦点问题

本书共十七章，概述了解析数论中的一些基本结果，发展并扩展了达文波特在论文中提出的一些思想，讨论的主题包括迪利克雷L—级数及其解析延拓和函数方程，包含了有关字符和γ函数的相关支撑的材料。本书还研究了当a和b互质时，存在无穷多个素数全等于已知a模b的迪利克雷定理和等差数列的素数定理，还讨论了如何将这些思想应用于所谓的负佩尔方程的理论之中，具体研究了迪利克雷特征、L—系列、γ函数、黎曼ζ函数、泊松求和公式、西格尔零点和算术级数中素数的迪利克雷定理等内容。

1 Introduction
1.1 Acknowledgements
2 Some Basics
3 Dirichlet Characters
3.1 The Orthogonality Relation of Dirichlet Characters
3.2 An Identity Involving Characters
4 L-Series
5 The Gamma Function
6 The Riemann Zeta-Function
6.1 Analytic Continuation of the Riemann zeta-function
6.2 The Riemann Hypothesis
7 The Functional Equation of L(s,x)
7.1 Gauss sums
7.2 The Functional Equation when X(-1) =1
7.3 The Functional Equation when X(-1) =-1
8 The Poisson Summation Formula
8.1 The Functional Equation for the Theta Function
9 Siegel Zeros
10 Dirichlet's Theorem on Primes in Arithmetic Progressions
10.1 An Important Result
10.2 The Proof of Dirichlet's Theorem
11 The Prime Number Theorem for Arithmetic Progressions
12 The yon Mangoldt Function
13 An Application of Analytic Number Theory:The Negative Pell Equation
13.1 Introduction
13.2 Strategy for Proving the Main Uniformity Assumption
14 The Maclaurin-Cauchy Integral Formula
15 An Important Lemma
16 Proof of The Main Uniformity Assumption
17 Further Reading On The Negative Pell Equation
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