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SIEGEL MODULAR FORMS AND RADIAL DIRICLET SERIES Anatoli Andrianov and Fedor Andrianov
 

Summary: SIEGEL MODULAR FORMS AND RADIAL DIRICLET SERIES
Anatoli Andrianov and Fedor Andrianov
Contents
Introduction: On arithmetical zeta functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Chapter 1. Modular forms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
§1.1. Symplectic group and upper half-plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
§1.2. Fundamental domains for modular group and related groups. . . . . . . . . . 12
§1.3. Modular forms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
§1.4. Petersson scalar product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Chapter 2. Radial Dirichlet series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . *
§2.1. Mellin transform of elliptic modular cusp forms. . . . . . . . . . . . . . . . . . . . . . . . *
§2.2. Radial Dirichlet series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . *
§2.3. Hyperbolic geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . *
§2.4. Integral representation of radial series for the sum of two squares . . . . . . *
Chapter 3 Hecke­Shimura rings and Hecke operators, . . . . . . . . . . . . . . . . . . . . . . . . . . *
Chapter 3. Zeta functions of modular forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . *
Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . *
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . *
1991 Mathematics Subject Classification. 11F46, 11F60, 11F66.
Key words and phrases. Hecke operators, Hecke-Shimura rings, Siegel modular forms, zeta

  

Source: Andrianov, Fedor - Steklov Mathematical Institute, Russian Academy of Sciences

 

Collections: Mathematics