A note on Chudnovsky's Fuchsian equations

Details A note on Chudnovsky's Fuchsian equations A note on Chudnovsky's Fuchsian equations

2010-11-03

arxiv.org/abs/1011.0925v3

Mathematics

Classical Analysis and ODEs

Major changes + new results; LaTeX, 19 pages, 1 table, no figures

Scientific paper

We show that four exceptional Fuchsian equations, each determined by the four parabolic singularities, known as Chudnovsky's equations, are transformed into each other by algebraic transformations. We describe the equivalence of these equations and their relatives on tori. The latter are the Fuchsian equations on elliptic curves and their equivalence is characterized by transcendental bi-single-valued transformations which are performed explicitly in terms of elliptic functions.

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