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A Truncated Integral of the Poisson Summation Formula

Jason Levy
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Abstract

Let $G$ be a reductive algebraic group defined over $\bQ$, with anisotropic centre. Given a rational action of $G$ on a finite-dimensional vector space $V$, we analyze the truncated integral of the theta series corresponding to a Schwartz-Bruhat function on $V(\bA)$. The Poisson summation formula then yields an identity of distributions on $V(\bA)$. The truncation used is due to Arthur.

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Jason Levy. 2000-03-06. A Truncated Integral of the Poisson Summation Formula. https://arxiv.org/abs/math/9601217

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