初等Dirichlet级数和模形式

出版时间：2011-6  出版社：科学  作者：希穆勒  页数：147  
Tag标签：无  

内容概要

希穆勒编著的《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。

书籍目录

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