作者：（美）詹森·万纳
页数：152
出版社：哈尔滨工业大学出版社
出版日期：2021
ISBN：9787560395258
电子书格式：pdf/epub/txt
内容简介
本书是一部英文版的解析数论专著。本书是解析数论的一些基本结果的概述,发展并扩展了像达文波特写的这一类论文中提出的思想.讨论的主题包括狄利克雷L级数及其解析延拓和函数方程,包括有关字符和y函数的相关支撑材料等.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(modb)的狄利克雷定理和等差数列的素数定理,然后,他们讨论了如何将这些思想应用于所谓的佩尔方程的理论之中.本书的基本内容如目录所列。
目录
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.l 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
编辑手记
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.l 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
编辑手记
