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arXiv · 2407.13599

Petersson Inner Products and Whittaker--Fourier Periods on Even Special Orthogonal and Symplectic Groups

Yeongseong Jo
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Abstract

In this article, we would like to formulate a relation between the square norm of Whittaker--Fourier coefficients on even special orthogonal and symplectic groups and Petersson inner products along with the critical value of $L$-functions up to constants. We follow the path of Lapid and Mao to reduce it to the conjectural local identity. Our strategy is based on the work of Ginzburg--Rallis--Soudry on automorphic descent. We present the analogue result for odd special orthogonal groups, which is conditional on unfolding Whittaker functions of descents.

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Yeongseong Jo. 2024-07-18. Petersson Inner Products and Whittaker--Fourier Periods on Even Special Orthogonal and Symplectic Groups. https://arxiv.org/abs/2407.13599

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