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We formulate a refined version of the global Gan–Gross–Prasad conjecture for general Bessel models, extending the work of Ichino–Ikeda and R. N. Harris in the co-rank 1 case. It is an explicit formula relating the automorphic period of Bessel type and the central value of certain  L -function. To support such conjecture, we provide two examples for pairsSO  5   ×   SO  2$\operatorname{SO}_{5}\times\operatorname{SO}_{2}$    andSO  6   ×   SO  3$\operatorname{SO}_{6}\times\operatorname{SO}_{3}$    (both co-rank 3) in the endoscopic case via theta lifting.

Refined global Gan–Gross–Prasad conjecture for Bessel periods