Differential equations associated with nonarithmetic Fuchsian groups
Algebraic Geometry
2014-02-26 v1 Number Theory
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.
Cite
@article{arxiv.0710.5277,
title = {Differential equations associated with nonarithmetic Fuchsian groups},
author = {Irene Bouw and Martin Moeller},
journal= {arXiv preprint arXiv:0710.5277},
year = {2014}
}