Genus theta series, Hecke operators and the basis problem for Eisenstein series
Number Theory
2007-05-23 v2
Abstract
We derive explicit formulas for the action of the Hecke operator 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.
Cite
@article{arxiv.math/0508613,
title = {Genus theta series, Hecke operators and the basis problem for Eisenstein series},
author = {Hidenori Katsurada and Rainer Schulze-Pillot},
journal= {arXiv preprint arXiv:math/0508613},
year = {2007}
}
Comments
23 pages, to appear in the proceedings of the conference to the memory of Tsuneo Arakawa, Tokyo 2004. Revised Dec 14,2005: typos removed, some formulations corrected