Gamma factors root numbers and distinction

Nadir Matringe; Omer Offen

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arXiv · 1607.01982

Gamma factors root numbers and distinction

Nadir Matringe·Omer Offen

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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.

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Nadir Matringe, Omer Offen. 2016-07-07. Gamma factors root numbers and distinction. https://arxiv.org/abs/1607.01982

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