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arXiv · 2312.04505

On the change of epsilon factors for symmetric square transfers under twisting and applications

Tathagata Mandal·Sudipa Mondal
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Abstract

Let us consider the symmetric square transfer of the automorphic representation $\pi$ associated to a modular form $f \in S_k(N,\epsilon)$. In this article, we study the variation of the epsilon factor of ${\mathrm{sym}}^2(\pi)$ 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 ${\mathrm{sym}}^2(\pi)$ is involved in the variation number, we compute it in terms of $N$.

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Tathagata Mandal, Sudipa Mondal. 2023-12-07. On the change of epsilon factors for symmetric square transfers under twisting and applications. https://doi.org/10.1007/s00605-025-02143-5

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