数论中的模函数和狄利克莱级数
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作者： （美）阿波斯托尔著
出 版 社：
出版时间： 2009-4-1字数：版次： 1页数： 204印刷时间：开本： 16开印次：纸张：I S B N ： 9787510004407包装： 平装目录
Chapter 1
Elliptic functions
1.1 Introduction
1.2 Doubly periodic functions
1.3 Fundamental pairs of periods
1.4 Elliptic functions
1.5 Construction of elliptic functions
1.6 The Weierstrass function
1.7 The Laurent expansion of near the origin
1.8 Differential equation satisfied by
1.9 The Eisenstein series and the invariants and
1.10 The numbers el, e2,e3
1.11 The discriminant
1.12 Klein's modular function J()
1.13 Invariance of J under unimodular transformations
1.14 The Fourier expansions ofg2() and g3()
1.15 The Fourier expansions of A() and J() Exercises for Chapter 1
Chapter 2 The Modular group and modular functions
2.1 M6bius transformations
2.2 The modular group F
2.3 Fundamental regions
2.4 Modular functions
2.5 Special values of J
2.6 Modular functions as rational functions of J
2.7 Mapping properties of J
2.8 Application to the inversion problem for Eisenstein series
2.9 Application to Picard's theorem Exercises for Chapter 2
Chapter 3The Dedekind eta function
3.1 Introduction
3.2 Siegers proof of Theorem 3.1
3.3 Infinite product representation for A(r)
3.4 The general functional equation for q(r)
3.5 Iseki's transformation formula
3.6 Deduction of Dedekind's functional equation from Iseki's formula
3.7 Properties of Dedekind sums
3.8 The reciprocity law for Dedekind sums
3.9 Congruence properties of Dedekind sums
3.10 The Eisenstein series G2(z) Exercises for Chapter
Chapter 4Conyruences for the coefficients of the modular function
4.1 Introduction
4.2 The subgroup Fo(q)
4.3 Fundamental region of Fo(p)
4.4 Functions automorphic under the subgroup Fo(p)
4.5 Construction of functions belonging to Fo(p)
……
Chapter 5Rademacher's series for the partition function
Chapter 6 Modular forms with multiplicative coefficients
Chapter 7 Kronecker's theorem with applications
Chapter 8 General dirichlet series and Bohr's equivalence theorem
Supplement to Chapter
Bibliography
Index of special symbols
Index
