Introduction to Siegel modular forms and Dirichlet series

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. Topicsinclude: -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; -the proof of analytical continuation and functional equation (under certain assumptions) for Euler products associated with modular forms of genus two. Will become a standard reference on the subject Intended for graduate students and keeps prerequisites to a minimum Gives provocative examples in the simplest and most accessible terms Author is an expert who has originated many important ideas in the subject INDICE: Preface.- Introduction: The Two Features of Arithmetical Zeta Functions.- Modular Forms.- Dirichlet Series of Modular Forms.- Hecke-Shimura Rings of Double Cosets.- Hecke Operators.- Euler Factorization of Radial Series.- Conclusion: Other Groups, Other Horizons.- Notes.- Short Bibliography.-

• ISBN: 978-0-387-78752-7
• Editorial: Springer
• Encuadernacion: Rústica
• Páginas: 210
• Fecha Publicación: 01/12/2008
• Nº Volúmenes: 1
• Idioma: Inglés