2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74494We relate two parameter solutions of the sixth Painlevé equation and finite-gap solutions of the Heun equation by considering monodromy on a certain class of Fuchsian differential equations. In the appendix, we present formulae on differentials of elliptic modular functions, and obtain the ellitic form of the sixth Painlevé equation directly.17 pages, based on the talk given at the Workshop "Studies on elliptic integrable systems" (Kyoto, November 2004)Classical Analysis and ODEsMathematical PhysicsQuantum AlgebraExactly Solvable and Integrable Systems33E10,34M55text