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Genus theta series, Hecke operators and the basis problem for Eisenstein series

Hidenori Katsurada·Rainer Schulze-Pillot
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Abstract

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.

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Hidenori Katsurada, Rainer Schulze-Pillot. 2005-12-14. Genus theta series, Hecke operators and the basis problem for Eisenstein series. https://arxiv.org/abs/math/0508613

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