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Introduction to Siegel Modular Forms and Dirichlet Series (Universitext)
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ISBN
:
9780387787527
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Publisher
:
Springer
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Subject
:
Education, Mathematics
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Binding
:
PAPERBACK
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Pages
:
196
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Year
:
2008
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6397.0
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6141.0
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Description
This is intended for a graduate course on Siegel modular forms, Hecke operators, and related zeta functions. The authorx2019;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 include: * analytical properties of radial Dirichlet series attached to modular forms of genuses 1 and 2; * the abstract theory of Heckex2013;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. This text contains a number of exercises and the only prerequisites are standard courses in Algebra and Calculus (one and several variables).
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