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Abstract
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We establish an “automorphic version” of Deligne’s conjecture for motivic
-functions in the case of
Rankin–Selberg
-functions
of
over arbitrary
CM-fields
.
Our main results are of two different kinds: Firstly, for arbitrary integers
and suitable
pairs
of cohomological automorphic representations, we relate critical values of
with a product of Whittaker periods attached to
and
,
Blasius’s CM-periods of Hecke-characters and certain nonzero values of standard
-functions.
Secondly, these relations lead to quite broad generalizations of fundamental
rationality-results of Waldspurger, Harder and Raghuram, and others.
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Keywords
periods, rationality, special values, L-function,
Rankin–Selberg, GL(n)
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Mathematical Subject Classification
Primary: 11F67
Secondary: 11F70, 11G18, 11R39, 22E55
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Milestones
Received: 27 December 2019
Revised: 23 May 2020
Accepted: 14 June 2020
Published: 9 December 2020
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