A Truncated Integral of the Poisson Summation Formula

Details A Truncated Integral of the Poisson Summation Formula A Truncated Integral of the Poisson Summation Formula

1996-01-19

arxiv.org/abs/math/9601217v2

Mathematics

Number Theory

38 pages. More explanation given in difficult steps. Use made of a result of Brion-Vergne

Scientific paper

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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