Gamma Factors, Root Numbers, and Distinction

Matringe, Nadir ; Offen, Omer

Canadian journal of mathematics, Tome 70 (2018) no. 3, pp. 683-701

Résumé

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.

Détail

DOI : 10.4153/CJM-2017-011-6

Mots-clés : 11F70, distinguished representation, local constant

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