Euler Factorization of Radial Series

  • Anatoli AndrianovEmail author
Part of the Universitext book series (UTX)

Representations of symplectic Hecke–Shimura rings on spaces of modular forms given by Hecke operators provide a tool to approach the multiplicative properties of modular forms, which presumabl must reflect the multiplicative properties of the rings. It is not obvious in what terms the multiplicative properties of modular forms can be formulated, since the ordinary multiplication of the form leads out of the initial spaces and apparently has no relation to Hecke operators. One can ask instead, say, about multiplicative properties of Fourier coefficients of modular forms that are sets of complex numbers indexed by appropriate arithmetic sequences. For example, in the case of modular forms for the groups \(\Gamma_0^n(q)\)


Zeta Function Modular Form Fourier Coefficient Eisenstein Series Cusp Form 
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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Russian Academy of SciencesSteklov Institute of MathematicsPetersburgRussia

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