On Invariant Subspaces and Eigenfunctions for Regular Hecke Operators on Spaces of Multiple Theta Constants
نویسندگان
چکیده
Invariant subspaces and eigenfunctions for regular Hecke operators actinng on spaces spanned by products of even number of Igusa theta constants with rational characteristics are constructed. For some of the eigenfunctions of genuses g = 1 and 2, the corresponding zeta functions of Hecke and Andrianov are explicitely calculated.
منابع مشابه
Action of Hecke Operators on Theta-functions with Rational Characteristics
The explicit formulas for the transformation of theta-functions of integral positive definite quadratic forms under the action of regular Hecke operators, obtained in the author’s earlier paper (1996), are converted to transformation formulas for the theta-functions with rational characteristics (the theta-series) viewed as Siegel modular forms. As applications, sequences of invariant subspaces...
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