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Preface V
Introduction 1
Preliminaries on Modular Forms and Dirichlet Series 5
Basic symbols and the definition of modular forms 5
Elementary Fourier analysis 13
The functional equation of a Dirichlet series 19
Critical Values of Dirichlet L-functions 25
The values of elementary Dirichlet series at integers 25
The class number of a cyclotomic field 39
Some more formulas for L(k, x) 45
The Case of Imaginary Quadratic Fields and Nearly Holomorphic Modular Forms 53
Dirichlet series associated with an imaginary quadratic field 53
Nearly holomorphic modular forms 55
Eisenstein Series 59
Fourier expansion of Eisenstein series 59
Polynomial relations between Eisenstein series 66
Recurrence formulas for the critical values of certain Dirichlet series 75
Critical Values of Dirichlet Series Associated with Imaginary Quadratic Fields 79
The singular values of nearly holomorphic forms 79
The critical values of L-functions of an imaginary quadratic field 84
The zeta function of a member of a one-parameter family of elliptic curves 96
Supplementary Results 113
Isomorphism classes of abelian varieties with complex multiplication 113
The general case 113
The case of elliptic curves 117
Holomorphic differential operators on the upper half plane 120
Appendix 127
Integration and differentiation under the integral sign 127
Fourier series with parameters 130
The confluent hypergeometric function 131
The Weierstrass [Characters not reproducible]-function 136
The action of G[subscript A+] on modular forms 139
References 145
Index 147
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Add Elementary Dirichlet Series and Modular Forms, The main topics of the book are the critical values of Dirichlet L-functions and Hecke L-functions of an imaginary quadratic field, and various problems on elliptic modular forms. As to the values of Dirichlet L-functions, all previous papers and books re, Elementary Dirichlet Series and Modular Forms to the inventory that you are selling on WonderClubX
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Add Elementary Dirichlet Series and Modular Forms, The main topics of the book are the critical values of Dirichlet L-functions and Hecke L-functions of an imaginary quadratic field, and various problems on elliptic modular forms. As to the values of Dirichlet L-functions, all previous papers and books re, Elementary Dirichlet Series and Modular Forms to your collection on WonderClub |