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arXiv · 2610.25706

Rational Points on Drinfeld Modular Curves of Prime Level

Ryotaro Sakamoto
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Abstract

Let $q \ge 3$ be a prime power and let $\mathfrak{p} \subset \mathbf{F}_q[T]$ be a nonzero prime ideal of degree $d$. We prove that $Y_0(\mathfrak{p})(\mathbf{F}_q(T))=\emptyset$ if $d \ge 4$ is even or $d>q$, and that $Y_1(\mathfrak{p})(\mathbf{F}_q(T)) = \emptyset $ for every $d \ge 3$.

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BibTeXRIS

Ryotaro Sakamoto. 2026-10-19. Rational Points on Drinfeld Modular Curves of Prime Level. https://arxiv.org/abs/2610.25706

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