Modular Functions and Dirichlet Series in Number Theory
Modular Functions and Dirichlet Series in Number Theory
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DOI：
10.1007/978-1-4684-9910-0
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发表时间：
1976
期刊：
影响因子：
--
通讯作者：
T. Apostol
中科院分区：
文献类型：
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作者：
T. Apostol
这是一本两卷本教科书的第二卷，它是从加州理工学院过去25年开设的一门课程（数学160）演变而来的，第二卷的前提是与第一卷相当的数论背景知识，以及复分析的基本概念。本卷的大部分内容是专门讨论椭圆函数和模函数及其一些数论应用。其中的主要议题是Rademacher的收敛系列的分区函数，莱纳的同余式的傅立叶系数的模块化函数j（r），和赫克的理论，整个形式与乘法傅立叶系数。最后一章介绍了玻尔关于一般狄利克雷级数的等价理论。
This is the second volume of a 2-volume textbook* which evolved from a course (Mathematics 160) offered at the California Institute of Technology du ring the last 25 years.The second volume presupposes a background in number theory comparable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. Most of the present volume is devoted to elliptic functions and modular functions with some of their number-theoretic applications. Among the major topics treated are Rademacher's convergent series for the partition function, Lehner's congruences for the Fourier coefficients of the modular functionj (r), and Hecke's theory of entire forms with multiplicative Fourier coefficients. The last chapter gives an account of Bohr's theory of equivalence of general Dirichlet series.