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A local-global question in automorphic forms

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Title A local-global question in automorphic forms
 
Creator ANANDAVARDHANAN, UK
PRASAD, D
 
Subject period integrals
locally distinguished representations
globally distinguished representations
base change
Asai lift
Asai L-function
central L-values
epsilon factors
fibers of functorial lifts
simultaneous non-vanishing of L-functions
DISTINGUISHED REPRESENTATIONS
SL(2)
GL(2)
CHARACTERS
SURFACES
TUNNELL
VALUES
CYCLES
 
Description In this paper, we consider the SL(2) analogue of two well-known theorems about period integrals of automorphic forms on GL(2): one due to Harder-Langlands-Rapoport about non-vanishing of period integrals on GL(2)(A F) of cuspidal automorphic representations on GL(2)(A(E)) where E is a quadratic extension of a number field F, and the other due to Waldspurger involving toric periods of automorphic forms on GL(2)(A(F)). In both these cases, now involving SL(2), we analyze period integrals on global L-packets; we prove that under certain conditions, a global automorphic L-packet which at each place of a number field has a distinguished representation, contains globally distinguished representations, and further, an automorphic representation which is locally distinguished is globally distinguished.
 
Publisher CAMBRIDGE UNIV PRESS
 
Date 2014-10-17T05:40:28Z
2014-10-17T05:40:28Z
2013
 
Type Article
 
Identifier COMPOSITIO MATHEMATICA, 149(6)959-995
http://dx.doi.org/10.1112/S0010437X12000772
http://dspace.library.iitb.ac.in/jspui/handle/100/16091
 
Language en