Petersson Inner Products and Whittaker--Fourier Periods on Even Special Orthogonal and Symplectic Groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910533795446784 |
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| author | Jo, Yeongseong |
| author_facet | Jo, Yeongseong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13599 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Petersson Inner Products and Whittaker--Fourier Periods on Even Special Orthogonal and Symplectic Groups Jo, Yeongseong Number Theory Representation Theory 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. |
| title | Petersson Inner Products and Whittaker--Fourier Periods on Even Special Orthogonal and Symplectic Groups |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2407.13599 |