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 *-function A5. The action of G_A+ on modular forms References Index
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