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On the Gan-Gross-Prasad conjecture and its refinement for $\left(\mathrm{U}\left(2n\right),\mathrm{U}\left(1\right)\right)$ (2205.09471v2)

Published 19 May 2022 in math.NT and math.RT

Abstract: We prove the Gan-Gross-Prasad conjecture for $\left(\mathrm{U}\left(2n\right),\mathrm{U}\left(1\right)\right)$ in general and prove its refinement, namely the Ichino-Ikeda type explicit formula for the central $L$-values, under certain assumptions. Similarly, we also prove its split analogue, namely the Gan-Gross-Prasad conjecture and its refinement for $\left(\mathrm{GL}_{2n}, \mathrm{GL}_1\right) $ in general.

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