新書推薦：
《
最后一件大事
》
售價：NT$
296
《
镜鉴日本：日本经济的经验与教训
》
售價：NT$
403
《
资产配置行动指南
》
售價：NT$
296
《
书籍的社会史-中华帝国晚期的书籍与士人文化（第二版）
》
售價：NT$
403
《
活出主体性
》
售價：NT$
352
《
中国城市复兴
》
售價：NT$
653
《
踏入她们的河流
》
售價：NT$
449
《
绿镜头——非洲
》
售價：NT$
449
|
| 內容簡介： |
本书主要介绍数论中的基础理论与重要方法，同时兼顾数论的发展动态与前沿理论，重点围绕素数的性质、算术函数、同余理论、二次剩余理论、丢番图方程等知识体系与思想方法进行论述，注重对数论中更为高阶的理论，如黎曼zeta函数、素数定理、算术级数中的素数定理、指数和的估计、加性数论、大筛法及其应用等进行全方位、多角度、深层次的解读与阐述。本书对数论解析理论进行了全面而透彻的分析，如对有界素数间隔问题、华林问题的最新研究动态等进行了较为深入而全面的探讨，力图展现数论内部高度的统一性，呈现数论各个分支理论之间的紧密联系。
本书适合数学专业高年级本科生、研究生阅读，也可供广大数论学习爱好者参考阅读。
|
| 關於作者： |
华国栋
Hua Guodong is a distinguished professor who comes from the Department of Pure Mathematics of Weinan Normal University， focusing on number theory in a broad sense. He mainly concentrates on analytic number theory and its applications， especially in the classical number-theoretic fields， such as Riemann ζ-function， multiplicative number theory， exponential sums， sieve methods， additive number theory and algebraic number theory. His research also covers the wide-ranging topics in modern number theory， including automorphic forms and L-functions， elliptic curves， dynamic systems towards number theory， and more generally related fields associated with number-theoretic problems. As a young and promising scholar in number theory， he has published over 50 high-quality academic research papers in prestigious scholarly publications， many of which produce wide and significant impact on the corresponding topics. He endeavours to carry out curiosity-driven mathematical researches extensively and rigorously， and also strives to permeate great and original contributions to analytic number theory， especially focusing on the major and significant mathematical challenges unsolved or partly solved. Furthermore， he is also an honourable member of Chinese Mathematical Society， and the Reviewer for Mathematical Reviews associated to American Mathematical Society.
|
| 目錄：
|
Chapter 1 Prime Numbers
1.1 Divisibility
1.2 The Fundamental Theorem of Arithmetic
1.3 The Infinite of Primes
1.4 The Linear Diophantine Equations
Chapter 2 Arithmetic Functions
2.1 Multiplicative Functions
2.2 Dirichlet Convolution
2.3 The Divisor Function
2.4 Euler Totient Function
2.5 The Mobius Function
2.6 The von Mangoldt Function
2.7 The Mean Value of Arithmetic Functions
2.8 The Normal Order of Arithmetic Functions
Chapter 3 Congruences
3.1 Congruence Classes
3.2 Chinese Remainder Theorem
3.3 Euler Theorem and Fermat Little Theorem
3.4 Wilson Theorem
Chapter 4 Quadratic Reciprocity
4.1 Primitive Roots
4.2 Quadratic Residues
4.3 The Quadratic Reciprocity Law
4.4 Jacobi Symbol
Chapter 5 Diophantine Equation
5.1 Lagrange Four Square Theorem
5.2 Rational Points on Conics
5.3 Fermat Descent Method
5.4 Curves of Higher Degree
Chapter 6 Riemann Zeta-Function
6.1 Dirichlet Series
6.2 Perron Formula
6.3 Fundamental Properties of ζ(s)
6.4 Gamma Function
6.5 Functional Equation
6.6 Zeros of ζ(s)
6.7 Explicit Formula for ψ(x)
6.8 Further Applications
Chapter 7 The Prime Number Theorem
7.1 Chebyshev Theorems
7.2 Prime Counting Functions
7.3 Elementary Methods
7.4 Analytic Methods
Chapter 8 Primes in Arithmetic Progressions
8.1 Dirichlet Character
8.2 Dirichlet L-Function
8.3 Explicit Formula for ψ(x， χ)
8.4 Dirichlet Theorem
Chapter 9 Exponential sums
9.1 Equdistribution
9.2 Quadratures
Chapter 10 The Additive Number Theory
10.1 General Introduction
10.2 The Goldbach-Vinogradov Theorem
10.3 Binary Goldbach Conjecture
Chapter 11 The Large Sieve and Its Applications
11.1 Bilinear Forms and Large Sieve
11.2 The Bombieri-Vinogradov Theorem
Chapter 12 Sieve Methods and Their Applications
12.1 Set-up for General Sieves
12.2 Probability Background
12.3 Brun-Hooley Sieve
12.4 Selberg Sieve
12.5 The Web of Shifted Primes
12.6 GPY Sieve
12.7 Bounded Gaps Between Primes
12.8 Weighted Sieve
12.9 The Binary Goldbach Conjecture Revisited
12.10 Large Gaps Between Primes
Chapter 13 Automorphic Forms and L-Functions
13.1 Elliptic Functions
13.2 Modular Forms and L-Functions
13.3 Automorphic L-Functions
13.4 The Distributions of Hecke Eigenvalues
13.5 Standard L-Functions
Chapter 14 Further Topics and Beyond
14.1 Mobius Randomness Conjecture
References
|
|
購物車/收銀台(0) | 在線留言板
| 付款方式
| 聯絡我們
| 運費計算
| 幫助中心 |
加入書簽
HOME
新書上架
