Elementary Dirichlet series and modular forms /
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| Author / Creator: | Shimura, Goro, 1930-2019 |
|---|---|
| Imprint: | New York : Springer, c2007. |
| Description: | viii, 147 p. ; 25 cm. |
| Language: | English |
| Series: | Springer monographs in mathematics |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/6635809 |
Table of Contents:
- 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 half plane
- Appendix
- A1. Integration and differentiation under the integral sign
- A2. Fourier series with parameters
- A3. The confluent hypergeometric function
- A4. The Weierstrass [Characters not reproducible]-function
- A5. The action of G[subscript A+] on modular forms
- References
- Index
