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On endoscopy and the refined Gross–Prasad conjecture for (SO5, SO4)

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  05 August 2010

Wee Teck Gan  and
Atsushi Ichino
Wee Teck Gan
Affiliation:
Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, USA (wgan@math.ucsd.edu)
Atsushi Ichino
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan (ichino@sci.osaka-cu.ac.jp)
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Abstract

We prove an explicit formula for periods of certain automorphic forms on SO5 × SO4 along the diagonal subgroup SO4 in terms of L-values. Our formula also involves a quantity from the theory of endoscopy, as predicted by the refined Gross–Prasad conjecture.

Keywords

periods of automorphic formsL-valuesendoscopythe Gross–Prasad conjecture

MSC classification

Secondary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 10 , Issue 2 , April 2011 , pp. 235 - 324
Copyright
Copyright © Cambridge University Press 2010

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