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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.04505 |
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Table of 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 $N$.