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Gamma Factors, Root Numbers, and Distinction
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- Journal:
- Canadian Journal of Mathematics / Volume 70 / Issue 3 / 01 June 2018
- Published online by Cambridge University Press:
- 20 November 2018, pp. 683-701
- Print publication:
- 01 June 2018
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- Article
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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.
