On the change of epsilon factors for symmetric square transfers under twisting and applications
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910167528898560 |
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| author | Mandal, Tathagata Mondal, Sudipa |
| author_facet | Mandal, Tathagata Mondal, Sudipa |
| contents | Let us consider the symmetric square transfer of the automorphic representation $π$ associated to a modular form $f \in S_k(N,ε)$. In this article, we study the variation of the epsilon factor of ${\mathrm{sym}}^2(π)$ under twisting in terms of the local Weil-Deligne representation at each prime $p$. As an application, we detect the possible types of the symmetric square transfer of the local representation at $p$. Furthermore, as the conductor of ${\mathrm{sym}}^2(π)$ is involved in the variation number, we compute it in terms of $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04505 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the change of epsilon factors for symmetric square transfers under twisting and applications Mandal, Tathagata Mondal, Sudipa Number Theory Let us consider the symmetric square transfer of the automorphic representation $π$ associated to a modular form $f \in S_k(N,ε)$. In this article, we study the variation of the epsilon factor of ${\mathrm{sym}}^2(π)$ under twisting in terms of the local Weil-Deligne representation at each prime $p$. As an application, we detect the possible types of the symmetric square transfer of the local representation at $p$. Furthermore, as the conductor of ${\mathrm{sym}}^2(π)$ is involved in the variation number, we compute it in terms of $N$. |
| title | On the change of epsilon factors for symmetric square transfers under twisting and applications |
| topic | Number Theory |
| url | https://arxiv.org/abs/2312.04505 |