A note on Chudnovsky's Fuchsian equations
Classical Analysis and ODEs
2012-10-16 v4 Exactly Solvable and Integrable Systems
Abstract
We show that four exceptional Fuchsian equations, each determined by the four parabolic singularities, known as the Chudnovsky equations, are transformed into each other by algebraic transformations. We describe equivalence of these equations and their counterparts on tori. The latter are the Fuchsian equations on elliptic curves and their equivalence is characterized by transcendental transformations which are represented explicitly in terms of elliptic and theta functions.
Cite
@article{arxiv.1011.0925,
title = {A note on Chudnovsky's Fuchsian equations},
author = {Yu. V. Brezhnev},
journal= {arXiv preprint arXiv:1011.0925},
year = {2012}
}
Comments
Final version; LaTeX, 27 pages, 1 table, no figures