On Transformation properties of hypergeometric motives and Diophantine equations

TL;DR

This paper explores the arithmetic analogues of classical hypergeometric function transformations and demonstrates their application in solving certain Diophantine equations.

Contribution

It introduces the study of transformation properties of hypergeometric motives and applies these to analyze specific Diophantine equations.

Findings

Transformation properties of hypergeometric motives are characterized.

Application of these properties to solve Diophantine equations.

New insights into the arithmetic structure of hypergeometric functions.

Abstract

Over the last two hundred years different transformation formulas for Gauss' hypergeometric function ${}_2F_1$ 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.