We give a sufficient condition on a pair of (primitive) polynomials that the associated hypergeometric group (monodromy group of the corresponding hypergeometric differential equation) is an arithmetic subgroup of the integral symplectic group.
"Arithmeticity of certain symplectic hypergeometric groups." Duke Math. J. 163 (3) 591 - 617, 15 February 2014. https://doi.org/10.1215/00127094-2410655