初等Dirichlet級(jí)數(shù)和模形式

出版時(shí)間:2011-6  出版社:科學(xué)  作者:希穆勒  頁數(shù):147  
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內(nèi)容概要

希穆勒編著的《初等Dirichlet級(jí)數(shù)和模形式(影印版)》是“國外數(shù)學(xué)名著系列”之一,介紹了初等Dirichlet級(jí)數(shù)和模形式、Eisentein級(jí)數(shù)、DirichletL-函數(shù)的臨界值、Dirichlet級(jí)數(shù)的臨界值和虛二次域的關(guān)系等。可供高等院校數(shù)學(xué)系研究生、數(shù)學(xué)科研人員學(xué)習(xí)參考。

書籍目錄

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

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