Petersson Inner Products and Whittaker--Fourier Periods on Even Special Orthogonal and Symplectic Groups
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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.13599
- arXiv:
- arXiv:2407.13599
- Bibcode:
- 2024arXiv240713599J
- Keywords:
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- Mathematics - Number Theory;
- Mathematics - Representation Theory
- E-Print:
- 44 pages