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初等Dirichlet级数和模形式
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资料介绍
初等Dirichlet级数和模形式
出版时间：2011年版
内容简介
《初等Dirichlet级数和模形式（影印版）》介绍了初等Dirichlet级数和模形式、Eisentein级数、DirichletL-函数的临界值、Dirichlet级数的临界值和虚二次域的关系等。《初等Dirichlet级数和模形式（影印版）》是“国外数学名著系列”之一，介绍了初等Dirichlet级数和模形式、Eisentein级数、DirichletL-函数的临界值、Dirichlet级数的临界值和虚二次域的关系等。可供高等院校数学系研究生、数学科研人员学习参考。
目录
Preface
Introduction
Chapter I. Preliminaries on Modular Forms and Dirichlet Series
1.Basic symbols and the definition of modular forms
2.Elementary Fourier analysis
3.The functional equation of a Dirichlet series
Chapter II.Critical Values of Dirichlet L-functions
4.The values of elementary Dirichlet series at integers
5.The class number of a cyclotomic field
6.Some more formulas for L(k, X)
Chapter III.The Case of Imaginary Quadratic Fields and Nearly Holomorphic Modular Forms
7.Dirichlet series associated with an imaginary quadratic field
8.Nearly holomorphic modular forms
Chapter IV.Eisenstein Series
9.Fourier expansion of Eisenstein series
10. Polynomial relations between Eisenstein series
11. Recurrence formulas for the critical values of certain Dirichlet series
Chapter V.Critical Values of Dirichlet Series Associated with Imaginary Quadratic Fields
12. The singular values of nearly holomorphic forms
13. The critical values of L-functions of an imaginary quadratic field
14.The zeta function of a member of a one-parameter family of elliptic curves
Chapter VI.Supplementary Results
15. Isomorphism classes of abelian varieties with complex multiplication
15A. The general case
15B. The case of elliptic curves
16. Holomorphic differential operators on the upper halfplane
Appendix
A1. Integration and differentiation under the integral sign
A2. Fourier series with parameters
A3. The confluent hypergeometric function
A4. The Weierstrass gg-function
A5. The action of GA+ on modular forms
References
Index
出版时间：2011年版
内容简介
《初等Dirichlet级数和模形式（影印版）》介绍了初等Dirichlet级数和模形式、Eisentein级数、DirichletL-函数的临界值、Dirichlet级数的临界值和虚二次域的关系等。《初等Dirichlet级数和模形式（影印版）》是“国外数学名著系列”之一，介绍了初等Dirichlet级数和模形式、Eisentein级数、DirichletL-函数的临界值、Dirichlet级数的临界值和虚二次域的关系等。可供高等院校数学系研究生、数学科研人员学习参考。
目录
Preface
Introduction
Chapter I. Preliminaries on Modular Forms and Dirichlet Series
1.Basic symbols and the definition of modular forms
2.Elementary Fourier analysis
3.The functional equation of a Dirichlet series
Chapter II.Critical Values of Dirichlet L-functions
4.The values of elementary Dirichlet series at integers
5.The class number of a cyclotomic field
6.Some more formulas for L(k, X)
Chapter III.The Case of Imaginary Quadratic Fields and Nearly Holomorphic Modular Forms
7.Dirichlet series associated with an imaginary quadratic field
8.Nearly holomorphic modular forms
Chapter IV.Eisenstein Series
9.Fourier expansion of Eisenstein series
10. Polynomial relations between Eisenstein series
11. Recurrence formulas for the critical values of certain Dirichlet series
Chapter V.Critical Values of Dirichlet Series Associated with Imaginary Quadratic Fields
12. The singular values of nearly holomorphic forms
13. The critical values of L-functions of an imaginary quadratic field
14.The zeta function of a member of a one-parameter family of elliptic curves
Chapter VI.Supplementary Results
15. Isomorphism classes of abelian varieties with complex multiplication
15A. The general case
15B. The case of elliptic curves
16. Holomorphic differential operators on the upper halfplane
Appendix
A1. Integration and differentiation under the integral sign
A2. Fourier series with parameters
A3. The confluent hypergeometric function
A4. The Weierstrass gg-function
A5. The action of GA+ on modular forms
References
Index
