[夸克网盘]初等Dirichlet级数和模形式-72-(影印版) PDF

PrefaceIntroductionChapter 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 seriesChapter 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 NearlyHolomorphic Modular Forms 7.Dirichlet series associated with an imaginary quadratic field 8.Nearly holomorphic modular formsChapter IV.Eisenstein Series 9.Fourier expansion of Eisenstein series 10. Polynomial relations between Eisenstein series 11. Recurrence formulas for the critical values of certainDirichlet seriesChapter V.Critical Values of Dirichlet Series Associated withImaginary Quadratic Fields 12. The singular values of nearly holomorphic forms 13. The critical values of L-functions of an imaginary quadraticfield 14.The zeta function of a member of a one-parameter family ofelliptic curvesChapter VI.Supplementary Results 15. Isomorphism classes of abelian varieties with complexmultiplication 15A. The general case 15B. The case of elliptic curves 16. Holomorphic differential operators on the upper halfplaneAppendix 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 formsReferencesIndex