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# Gamma Factors, Root Numbers, and Distinction

Published:2018-01-11
Printed: Jun 2018
Laboratoire de Mathématiques et Applications Téléport 2-BP 30179, 11 Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil Cedex, France
• Omer Offen,
Department of Mathematics, Technion, Israel Institute of Technology , Haifa 3200003, Israel
 Format: LaTeX MathJax PDF

## Abstract

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: distinguished representation, local constant
 MSC Classifications: 11F70 - Representation-theoretic methods; automorphic representations over local and global fields

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