Arithmeticity of Some Hypergeometric Groups

Abstract

We show that the hypergeometric groups associated to the pairs of the parameters $\left(0,0,\frac{1}{3}, \frac{2}{3}\right)$, $\left(\frac{1}{2},\frac{1}{2},\frac{1}{4},\frac{3}{4}\right)$; and $\left(0,\frac{1}{12}, \frac{5}{12},\frac{7}{12},\frac{11}{12}\right), \left(\frac{1}{2},\frac{1}{3},\frac{1}{3},\frac{2}{3},\frac{2}{3}\right)$ are arithmetic.