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A Truncated Integral of the Poisson Summation Formula

Published online by Cambridge University Press:  20 November 2018

Jason Levy
Jason Levy*
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, ON, K1N 6N5. email: jlevy@science.uottawa.ca
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Abstract

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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.

Keywords

11F9911F72
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 53 , Issue 1 , 01 February 2001 , pp. 122 - 160
Copyright
Copyright © Canadian Mathematical Society 2001

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