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

Recent work of Altuğ continues the preliminary analysis of Langlands' Beyond Endoscopy proposal for GL(2) by removing the contribution of the trivial representation by a Poisson summation formula. We show that Altuğ's method of smoothing real elliptic orbital integrals by an approximate fu...

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Bibliographic Details
Published in:Journal of number theory 2018-02, Vol.183, p.407-427
Main Authors: González, Oscar E., Kwan, Chung Hang, Miller, Steven J., Van Peski, Roger, Wong, Tian An
Format: Article
Language:English
Subjects:
Approximate functional equation
Beyond Endoscopy
Orbital integrals
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Summary:Recent work of Altuğ continues the preliminary analysis of Langlands' Beyond Endoscopy proposal for GL(2) by removing the contribution of the trivial representation by a Poisson summation formula. We show that Altuğ'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.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2017.08.004