Hecke operators on Hilbert–Siegel theta series
نویسندگان
چکیده
منابع مشابه
Action of Hecke Operators on Siegel Theta Series Ii
We apply the Hecke operators T (p) and T ′ j (p) (1 ≤ j ≤ n ≤ 2k) to a degree n theta series attached to a rank 2k Z-lattice L equipped with a positive definite quadratic form in the case that L/pL is regular. We explicitly realize the image of the theta series under these Hecke operators as a sum of theta series attached to certain sublattices of 1 p L, thereby generalizing the Eichler Commuta...
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We apply the Hecke operators T (p) and T̃j(p 2) (1 ≤ j ≤ n, p prime) to a degree n theta series attached to a rank 2k Z-lattice L, n ≤ k, equipped with a positive definite quadratic form in the case that L/pL is hyperbolic. We show that the image of the theta series under these Hecke operators can be realized as a sum of theta series attached to certain closely related lattices, thereby generali...
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The introductory part contains definitions and basic properties of harmonic theta series, Siegel modular forms, and Hecke operators. Then the transformation formulas are recalled, related to the action of modular substitutions and regular Hecke operators on general harmonic theta series, including specialization to the case of Maass theta series. The following new results are obtained: construc...
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We derive explicit formulas for the action of the Hecke operator T (p) on the genus theta series of a positive definite integral quadratic form and prove a theorem on the generation of spaces of Eisenstein series by genus theta series. We also discuss connections of our results with Kudla’s matching principle for theta integrals.
متن کاملAction 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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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2021
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s179304212150072x