Central Values of Degree Six L-functions: The Case of Hilbert Modular Forms
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866910781307617280 |
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| author | Agrawal, Utkarsh |
| author_facet | Agrawal, Utkarsh |
| contents | In this paper we give a formula for the central value of the completed $L$-function $L(s,Sym^{2} g\times f)$, where $f$ and $g$ are Hilbert newforms, by explicitly computing the local integrals appearing in the refined Gan-Gross-Prasad conjecture for $SL_{2}\times\tilde{SL_{2}}$. We also work out the rationality of this value in some special cases and give a conjecture for the general case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_05659 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Central Values of Degree Six L-functions: The Case of Hilbert Modular Forms Agrawal, Utkarsh Number Theory In this paper we give a formula for the central value of the completed $L$-function $L(s,Sym^{2} g\times f)$, where $f$ and $g$ are Hilbert newforms, by explicitly computing the local integrals appearing in the refined Gan-Gross-Prasad conjecture for $SL_{2}\times\tilde{SL_{2}}$. We also work out the rationality of this value in some special cases and give a conjecture for the general case. |
| title | Central Values of Degree Six L-functions: The Case of Hilbert Modular Forms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2110.05659 |