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# A Truncated Integral of the Poisson Summation Formula

Published:2001-02-01
Printed: Feb 2001
• 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.
 MSC Classifications: 11F99 - None of the above, but in this section 11F72 - Spectral theory; Selberg trace formula