On smoothing singularities of elliptic orbital integrals on GL(n) and Beyond Endoscopy

Oscar E. González; Chung Hang Kwan; Steven J. Miller; Roger Van Peski; Tian An Wong

On smoothing singularities of elliptic orbital integrals on GL(n) and Beyond Endoscopy

Number Theory 2017-09-14 v2 Representation Theory

Authors: Oscar E. González , Chung Hang Kwan , Steven J. Miller , Roger Van Peski , Tian An Wong

Abstract

Recent work of Altu\u{g} continues the preliminary analysis of Langlands' Beyond Endoscopy proposal for $GL(2)$ by removing the contribution of the trivial representation to the trace formula using a Poisson summation formula. We show that Altu\u{g}'s method of smoothing real elliptic orbital integrals by an approximate functional equation extends to $GL(n)$ . We also discuss the case of an arbitrary reductive group, and remaining obstructions for applying Poisson summation.

Keywords

elliptic orbital integrals Beyond Endoscopy trace formula Poisson summation approximate functional equation reductive groups Langlands program

Cite

@article{arxiv.1608.05938,
  title  = {On smoothing singularities of elliptic orbital integrals on GL(n) and Beyond Endoscopy},
  author = {Oscar E. González and Chung Hang Kwan and Steven J. Miller and Roger Van Peski and Tian An Wong},
  journal= {arXiv preprint arXiv:1608.05938},
  year   = {2017}
}

Comments

To appear in Journal of Number Theory

On smoothing singularities of elliptic orbital integrals on GL(n) and Beyond Endoscopy

Abstract

Keywords

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