A Truncated Integral of the Poisson Summation Formula

Jason Levy

A Truncated Integral of the Poisson Summation Formula

Number Theory 2008-02-03 v2

Authors: Jason Levy

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.

Keywords

reductive algebraic group poisson summation formula theta series truncated integral schwartz-bruhat function distribution identity

Cite

@article{arxiv.math/9601217,
  title  = {A Truncated Integral of the Poisson Summation Formula},
  author = {Jason Levy},
  journal= {arXiv preprint arXiv:math/9601217},
  year   = {2008}
}

Comments

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

A Truncated Integral of the Poisson Summation Formula

Abstract

Keywords

Cite

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