On the Gan-Gross-Prasad conjecture and its refinement for $\left(\mathrm{U}\left(2n\right),\mathrm{U}\left(1\right)\right)$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912075562876928 |
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| author | Furusawa, Masaaki Morimoto, Kazuki |
| author_facet | Furusawa, Masaaki Morimoto, Kazuki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_09471 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Gan-Gross-Prasad conjecture and its refinement for $\left(\mathrm{U}\left(2n\right),\mathrm{U}\left(1\right)\right)$ Furusawa, Masaaki Morimoto, Kazuki Number Theory Representation Theory 11F55, 11F67 (Primary) 11F27 (Secondary) 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. |
| title | On the Gan-Gross-Prasad conjecture and its refinement for $\left(\mathrm{U}\left(2n\right),\mathrm{U}\left(1\right)\right)$ |
| topic | Number Theory Representation Theory 11F55, 11F67 (Primary) 11F27 (Secondary) |
| url | https://arxiv.org/abs/2205.09471 |