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Automorphic period and the central value of Rankin-Selberg L-function


Author: Wei Zhang
Journal: J. Amer. Math. Soc. 27 (2014), 541-612
MSC (2010): Primary 11F67, 11F70, 22E55; Secondary 11G40, 22E50
DOI: https://doi.org/10.1090/S0894-0347-2014-00784-0
Published electronically: January 27, 2014
MathSciNet review: 3164988
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Abstract: Using the relative trace formula of Jacquet and Rallis, under some local conditions we prove a refinement of the global Gan-Gross-Prasad conjecture proposed by Ichino-Ikeda and N. Harris for unitary groups. We need to assume some expected properties of L-packets and some part of the local Gan-Gross-Prasad conjecture.


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Additional Information

Wei Zhang
Affiliation: Department of Mathematics, Columbia University, MC 4423, 2990 Broadway, New York, New York 10027
Email: wzhang@math.columbia.edu

DOI: https://doi.org/10.1090/S0894-0347-2014-00784-0
Keywords: Automorphic period, Rankin-Selberg L-function, the global Gan-Gross-Prasad conjecture, Ichino-Ikeda conjecture, Jacquet-Rallis relative trace formula, spherical character, local character expansion, regular unipotent orbital integral.
Received by editor(s): July 8, 2012
Received by editor(s) in revised form: January 4, 2013, April 14, 2013, and July 22, 2013
Published electronically: January 27, 2014
Additional Notes: The author was supported in part by NSF Grant #1204365 and a Sloan research fellowship.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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