初等Dirichlet级数和模形式

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

《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。