Genus theta series, Hecke operators and the basis problem for Eisenstein series
Hidenori Katsurada, Rainer Schulze-Pillot
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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