On Transformation properties of hypergeometric motives and Diophantine equations

Abstract

Over the last two hundred years different transformation formulas for Gauss' hypergeometric function ${}_2{F}_1$ were discovered. The goal of the present article is to study their arithmetic analogue for the underlying hypergeometric motive. As an application, we show how these transformation properties can be used in the study of some Diophantine equations.

17 pages