Differential equations associated with nonarithmetic Fuchsian groups
Differential equations associated with nonarithmetic Fuchsian groups
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与非算术 Fuchsian 群相关的微分方程
DOI：
10.1112/jlms/jdp059
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Martin Moeller
中科院分区：
文献类型：
--
作者：
I. Bouw;Martin Moeller
我们描述了定义在单群为非算术Fuchsian群的数域上的全局二阶幂零微分算子。我们证明了这些微分算子有？的整体解决方案。这些微分算子自然地与2属曲线的模空间中的teichm<s:1> ller曲线联系在一起。它们是Chudnovsky-Chudnovsky和Dwork猜想的反例。我们还在2属曲线的模空间中确定了原始teichmller曲线的模域，并在某些情况下给出了显式方程。
We describe globally nilpotent differential operators of rank 2 defined over a number field whose monodromy group is a nonarithmetic Fuchsian group. We show that these differential operators have an ?‐integral solution. These differential operators are naturally associated with Teichmüller curves in the moduli space of curves of genus 2. They are counterexamples to conjectures by Chudnovsky–Chudnovsky and Dwork. We also determine the field of moduli of primitive Teichmüller curves in the moduli space of curves of genus 2, and an explicit equation in some cases.