wreaths
introduction to siegel modular forms and dirichlet series
p 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 . p topics include p analytical properties of radial dirichlet series attached to modular forms of genuses 1 and 2 ; p the abstract theory of hecke shimura rings for symplectic and related groups ; p action of hecke operators on siegel modular forms ; p applications of hecke operators to a study of multiplicative properties of fourier coefficients of modular forms ; p hecke zeta functions of modular forms in one variable and to spinor or andrianov zeta functions of siegel modular forms of genus two ; p the proof of analytical continuation and functional equation under certain assumptions for euler products associated with modular forms of genus two . p this text contains a number of exercises and the only prerequisites are standard courses in algebra and calculus one and several variables .