在Bring曲线上计算代数Belyi函数

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2025-09-05 DOI:10.1007/s00013-025-02174-2

Madoka Horie, Takuya Yamauchi

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引用次数: 0

摘要

本文明确地计算了Bring曲线上的两类代数Belyi函数。一个与\(\textrm{SL}_2({\mathbb {Z}})\)的同余子群有关，另一个与三角形群的同余子群有关\(\Delta (2,4,5)\subset \textrm{SL}_2({\mathbb {R}}).\)的同余子群有关。为了进行计算，我们对前者使用权值为2的椭圆尖形，对后者使用Bring曲线的自同态群。我们还讨论了描述Hulek-Craig曲线、Bring曲线和另一个作为模曲线得到的代数模型之间同构的合适基域（数域）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Computing algebraic Belyi functions on Bring’s curve

In this paper, we explicitly compute two kinds of algebraic Belyi functions on Bring’s curve. One is related to a congruence subgroup of \(\textrm{SL}_2({\mathbb {Z}})\) and the other is related to a congruence subgroup of the triangle group \(\Delta (2,4,5)\subset \textrm{SL}_2({\mathbb {R}}).\) To carry out the computation, we use elliptic cusp forms of weight 2 for the former case and the automorphism group of Bring’s curve for the latter case. We also discuss a suitable base field (a number field) for describing isomorphisms between Hulek–Craig’s curve, Bring’s curve, and another algebraic model obtained as a modular curve.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.