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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2201.03270 |
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| _version_ | 1866909163561418752 |
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| author | Haan, Jaeho |
| author_facet | Haan, Jaeho |
| contents | 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 $GL_{2n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_03270 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Fourier-Jacobi Periods : The case of $Mp(2n+2r) \times Sp(2n)$ Haan, Jaeho Number Theory Representation Theory 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 $GL_{2n}$. |
| title | The Fourier-Jacobi Periods : The case of $Mp(2n+2r) \times Sp(2n)$ |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2201.03270 |