The symplectic period of certain Eisenstein series on GL(2n+1) matches the L-function ratio predicted by relative Langlands duality, confirming the dual pair Sp(2n)\GL(2n+1) and GL(n)xGL(n+1)\GL(2n+1) in the tested cases.
Vanishing periods of cusp forms over modular symbols
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On the relative Langlands duality for $\operatorname{Sp}_{2n} \backslash \operatorname{GL}_{2n+1}$ (with an appendix by Zeyu Wang)
The symplectic period of certain Eisenstein series on GL(2n+1) matches the L-function ratio predicted by relative Langlands duality, confirming the dual pair Sp(2n)\GL(2n+1) and GL(n)xGL(n+1)\GL(2n+1) in the tested cases.