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Introduction to Siegel Modular Forms and Dirichlet Series

Introduction to Siegel Modular Forms and Dirichlet Series
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Field name Details
Dewey Class 512.7
Title Introduction to Siegel Modular Forms and Dirichlet Series (EB) / by Anatoli Andrianov.
Author Andrianov, Anatoli Nikolaevich , 1936-
Other name(s) SpringerLink (Online service)
Publication New York, NY : Springer US , 2009.
Physical Details XII, 184 pages : online resource.
Series Universitext 0172-5939
ISBN 9780387787534
Summary Note Introduction to Siegel Modular Forms and Dirichlet Series gives a concise and self-contained introduction to the multiplicative theory of Siegel modular forms, Hecke operators, and zeta functions, including the classical case of modular forms in one variable. It serves to attract young researchers to this beautiful field and makes the initial steps more pleasant. It treats a number of questions that are rarely mentioned in other books. It is the first and only book so far on Siegel modular forms that introduces such important topics as analytic continuation and the functional equation of spinor zeta functions of Siegel modular forms of genus two. Unique features include: * New, simplified approaches and a fresh outlook on classical problems * The abstract theory of Heckeââ¬âShimura rings for symplectic and related groups * The action of Hecke operators on Siegel modular forms * Applications of Hecke operators to a study of the multiplicative properties of Fourier coefficients of modular forms * The proof of analytic continuation and the functional equation (under certain assumptions) for Euler products associated with modular forms of genus two *Numerous exercises Anatoli Andrianov is a leading researcher at the St. Petersburg branch of the Steklov Mathematical Institute of the Russian Academy of Sciences. He is well known for his works on the arithmetic theory of automorphic functions and quadratic forms, a topic on which he has lectured at many universities around the world.:
Contents note 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.-.
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