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arXiv · 0710.5277

Differential equations associated with nonarithmetic Fuchsian groups

Irene Bouw·Martin Moeller
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Abstract

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 S-integral solution. These differential operators are naturally associated with Teichmueller curves in genus 2. They are counterexamples to conjectures by Chudnovsky--Chudnovsky and Dwork. We also determine the field of moduli of primitive Teichmueller curves in genus 2, and an explicit equation in some cases.

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Irene Bouw, Martin Moeller. 2007-10-29. Differential equations associated with nonarithmetic Fuchsian groups. https://doi.org/10.1112/jlms%2Fjdp059

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