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Rational Points on Drinfeld Modular Curves of Prime Level
Abstract
Let q ≥ 3 be a prime power and let p ⊂ Fq[T] be a nonzero prime ideal of degree d. We prove that Y0(p)(Fq(T))=∅ if d ≥ 4 is even or d>q, and that $Y_1(\mathfrak{p})(\mathbf{F}_q(T)) = \emptyset $ for every d ≥ 3.
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BibTeX
@misc{sakamoto2026rational,
title = {{Rational Points on Drinfeld Modular Curves of Prime Level}},
author = {Ryotaro Sakamoto},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25706},
eprint = {2610.25706},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25706},
}
RIS
TY - UNPB
TI - Rational Points on Drinfeld Modular Curves of Prime Level
AU - Ryotaro Sakamoto
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25706
UR - https://arxiv.org/abs/2610.25706
AB - Let q ≥ 3 be a prime power and let p ⊂ F_q[T] be a nonzero prime ideal of degree d. We prove that Y_0(p)(F_q(T))=∅ if d ≥ 4 is even or d>q, and that $Y_1(\mathfrak{p})(\mathbf{F}_q(T)) = \emptyset $ for every d ≥ 3.
ER -