The Fourier-Jacobi Periods : The case of $Mp(2n+2r) \times Sp(2n)$
Abstract
In this paper, we prove one direction of the Gan--Gross--Prasad conjecture on metaplectic-symplectic groups for tempered cases. Furthermore, we also prove one direction of the non-tempered GGP conjecture for residual representations with relevant $A$-parameters. As an application, we discuss the non-vanishing of the central value of quadratic twists of automorphic $L$-functions of $GL_{2n}$.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2022
- DOI:
- arXiv:
- arXiv:2201.03270
- Bibcode:
- 2022arXiv220103270H
- Keywords:
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- Mathematics - Number Theory;
- Mathematics - Representation Theory
- E-Print:
- Rewritten various parts of the paper based on valuable feedback from the referee. The non-tempered cases are also included in Section 6