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

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Abstract

We prove a precise formula relating the Bessel period of certain automorphic forms on ${\rm GSp}{4}(\mathbb{A}{F})$to a central$L$-value. This is a special case of the refined Gan–Gross–Prasad conjecture for the groups$({\rm SO}{5},{\rm SO}{2})$as set out by Ichino–Ikeda and Liu. 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${\rm GL}{2}(\mathbb{A}{E})$where$E$is a quadratic extension of$F$. The case where$E=F\times F$ has been previously dealt with by Liu.

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URL

https://arxiv.org/abs/1507.00089

PDF

https://arxiv.org/pdf/1507.00089