THE MULTIPLICATIVE ARITHMETIC OR SIEGEL MODULAR FORMS

Abstract

CONTENTSIntroductionChapter 1. Hecke rings ??1.1. Definitions and general properties ??1.2. Hecke rings of the groups and Chapter 2. Decompositions of Hecke polynomials ??2.1. Centralizers of Frobenius elements ??2.2. Negative powers of Frobenius elements ??2.3. Decompositions of Hecke polynomials ??2.4. Decompositions of the polynomial ??2.5. A symmetric decomposition of Chapter 3. Representations of Hecke rings ??3.1. Siegel modular forms ??3.2. Hecke operators ??3.3. Hecke operators and the Siegel operator ??3.4. The operator polynomial Chapter 4. The action of Hecke operators on theta-series ??4.1. Theta-series ??4.2. Theta-representations of Hecke rings ??4.3. The action of Hecke operators on theta-series ??4.4. Eigenvalues of Hecke operators on spaces of theta-series ??4.5. Invariance of the generic theta-series and Siegel's theorem Chapter 5. The Euler decomposition of theta-transformations of Siegel modular forms ??5.1. The Euler decomposition of theta-transformations ??5.2. On analytic properties of zeta-functionsReferences