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Gamma Factors, Root Numbers, and Distinction

Published online by Cambridge University Press:  20 November 2018

Nadir Matringe  and
Omer Offen
Nadir Matringe
Affiliation:
Laboratoire de Mathématiques et Applications Téléport 2 - BP 30179, 11 Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil Cedex, France email: nadirmatringe@outlook.fr
Omer Offen
Affiliation:
Department of Mathematics, Technion, Israel Institute of Technology, Haifa 3200003, Israel email: offen@tx.technion.ac.il
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Abstract

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We study a relation between distinction and special values of local invariants for representations of the general linear group over a quadratic extension of $p$-adic fields. We show that the local Rankin–Selberg root number of any pair of distinguished representation is trivial, and as a corollary we obtain an analogue for the global root number of any pair of distinguished cuspidal representations. We further study the extent to which the gamma factor at 1/2 is trivial for distinguished representations as well as the converse problem.

Keywords

11F70distinguished representationlocal constant
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 70 , Issue 3 , 01 June 2018 , pp. 683 - 701
Copyright
Copyright © Canadian Mathematical Society 2018

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