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A Truncated Integral of the Poisson Summation Formula
Published online by Cambridge University Press: 20 November 2018
Abstract
Let $G$ be a reductive algebraic group defined over
$\mathbb{Q}$, 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
$V\left( \mathbb{A} \right)$. The Poisson summation formula then yields an identity of distributions on
$V\left( \mathbb{A} \right)$. The truncation used is due to Arthur.
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- Research Article
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- Copyright © Canadian Mathematical Society 2001
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