Heun functions and diagonals of rational functions (unabridged version)

Abstract

We provide a set of diagonals of simple rational functions of three and four variables that are squares of Heun functions. These Heun functions obtained through creative telescoping, turn out to be either pullbacked ${}_2{F}_1$ hypergeometric functions and in fact classical modular forms. We also obtain Heun functions that are Shimura curves as solutions of telescopers of rational functions.

64 pages

References in corpus (1)

• The Heun equation and the Calogero-Moser-Sutherland system IV: the Hermite-Krichever Ansatz