Commentary on Sp(6) hypergeometric groups

Abstract

We study the examples mentioned in [2,Tables A & C] and establish the arithmeticity of four examples of symplectic hypergeometric groups of degree six. Following [2] we know that there are 458 inequivalent symplectic hypergeometric groups of degree six, and combining the results of this article with the work of [1,2,11], we now know that at least 384 are arithmetic and at least 63 are thin whereas the arithmeticity and thinness of remaining 11 examples are still unknown.