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On Period Relations for Automorphic L-functions II · arXivDesk

1604.04253Apr 14, 2016updated references to "On Rational Structures on Automorphic Representations"

On Period Relations for Automorphic L-functions II

Fabian Januszewski

Abstract

We study Hecke algebras for pairs $({\mathfrak g},K)$ over arbitrary fields $E$ of characteristic $0$ , define the Bernstein functor and give another definition of the Zuckerman functor over $E$ . Building on this and the author's previous work on rational structures on automorphic representations, we show that hard duality remains valid over $E$

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and apply this result to the study of rationality properties of Sun's cohomologically induced functionals. Our main application are period relations for the special values of standard

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