A note on Chudnovsky's Fuchsian equations

[摘要] 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 latters 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. (C) 2012 Elsevier Inc. All rights reserved.

[发布日期] 2012-12-15

[关键词] Fuchsian Heun's equations;Hypergeometric functions;Punctured tori;Algebraic transformations;Algebraic curves;Transcendental covers;Theta-functions