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We provide a set of diagonals of simple rational functions of three and fourvariables that are squares of Heun functions. These Heun functions obtainedthrough creative telescoping, turn out to be either pullbacked $_2F_1$hypergeometric functions and in fact classical modular forms. We also obtainHeun functions that are Shimura curves as solutions of telescopers of rationalfunctions.

Heun functions and diagonals of rational functions (unabridged version)