A proof of the refined Gan–Gross–Prasad conjecture for non-endoscopic Yoshida lifts

Andrew J. Corbett

doi:10.1515/forum-2015-0164

Article

A proof of the refined Gan–Gross–Prasad conjecture for non-endoscopic Yoshida lifts

Published/Copyright: May 5, 2016

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From the journal Forum Mathematicum Volume 29 Issue 1

Abstract

We prove a precise formula relating the Bessel period of certain automorphic forms on GSp4⁢(𝔸F) to a central L-value. This is a special case of the refined Gan–Gross–Prasad conjecture for the groups (SO5,SO2) as set out by Ichino–Ikeda [12] and Liu [14]. This conjecture is deep and hard to prove in full generality; in this paper we succeed in proving the conjecture for forms lifted, via automorphic induction, from GL2⁢(𝔸E) where E is a quadratic extension of F. The case where E=F×F has been previously dealt with by Liu [14].

Keywords: Automorphic period integrals; the refined Gan–Gross–Prasadconjecture

MSC 2010: 11F67; 11F70

Communicated by Freydoon Shahidi

Acknowledgements

The author would like to offer sincere thanks to both Yifeng Liu, for his helpful comments and discussions, and Abhishek Saha, for his valuable guidance. Thanks are also due to Katharine Thornton for her many insightful suggestions.

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Received: 2015-8-31

Revised: 2016-1-29

Published Online: 2016-5-5

Published in Print: 2017-1-1

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https://doi.org/10.1515/forum-2015-0164

Keywords for this article

Automorphic period integrals; the refined Gan–Gross–Prasadconjecture