This is intended for a graduate course on Siegel modular forms, Hecke operators, and related zeta functions. The author's aim is to present a concise and self-contained introduction to an important and developing area of number theory that will ...
serve to attract young researchers to this beautiful field.Topics covered in this title include: analytical properties of radial "Dirichlet" series attached to modular forms of genuses 1 and 2; the abstract theory of Hecke - Shimura rings for symplectic and related groups; action of Hecke operators on Siegel modular forms; applications of Hecke operators to a study of multiplicative properties of Fourier coefficients of modular forms; Hecke zeta functions of modular forms in one variable and to spinor (or Andrianov) zeta functions of Siegel modular forms of genus two; and, the proof of analytical continuation and functional equation (under certain assumptions) for Euler products associated with modular forms of genus two. This text contains a number of exercises and the only prerequisites are standard courses in Algebra and Calculus (one and several variables).
Number of pages: 196
Date of publication: 01/10/2008
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