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Beyond endoscopy via the trace formula: 1. Poisson summation and isolation of special representations

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  01 June 2015

Salim Ali Altuğ
Salim Ali Altuğ*
Affiliation:
Mathematics Department, Columbia University, 2990 Broadway, New York, NY 10027, USA email altug@math.columbia.edu
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Abstract

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With analytic applications in mind, in particular beyond endoscopy, we initiate the study of the elliptic part of the trace formula. Incorporating the approximate functional equation into the elliptic part, we control the analytic behavior of the volumes of tori that appear in the elliptic part. Furthermore, by carefully choosing the truncation parameter in the approximate functional equation, we smooth out the singularities of orbital integrals. Finally, by an application of Poisson summation we rewrite the elliptic part so that it is ready to be used in analytic applications, and in particular in beyond endoscopy. As a by product we also isolate the contributions of special representations as pointed out in [Beyond endoscopy, in Contributions to automorphic forms, geometry and number theory (Johns Hopkins University Press, Baltimore, MD, 2004), 611–697].

Keywords

beyond endoscopytrace formula

MSC classification

Primary: 11F72: Spectral theory; Selberg trace formula
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 10 , October 2015 , pp. 1791 - 1820
Copyright
© The Author 2015 

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