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arXiv · 2503.22991

Root numbers for twisted Fermat quotient curves

Ryosuke Yanagihara
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Abstract

Let $\ell$ be an odd prime, $N \geq 1$ be an integer, and $\delta \geq 1$ be a $\ell^N$-th power free integer such that ${\rm ord}_{\ell}(\delta) = 0$ or $\ell \nmid {\rm ord}_{\ell}(\delta)$. In this paper, we give an explicit formula for the root number of the Hecke character associated with a certain quotient curve of the twisted Fermat curve $X^{\ell^N} + Y^{\ell^N} = \delta$. This result gives a generalization of Stoll (2002) and Shu (2021).

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Ryosuke Yanagihara. 2025-03-29. Root numbers for twisted Fermat quotient curves. https://arxiv.org/abs/2503.22991

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