A Truncated Integral of the Poisson Summation Formula

http://dx.doi.org/10.4153/CJM-2001-006-1
Canad. J. Math. 53(2001), 122-160

  Published:2001-02-01
 Printed: Feb 2001

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.