Roth's Theorem over arithmetic function fields

TL;DR

This paper extends Roth's theorem, a fundamental result in Diophantine approximation, to finitely generated field extensions of the rational numbers using Moriwaki's height framework.

Contribution

It introduces a novel extension of Roth's theorem to a broader class of fields via Moriwaki's height theory, expanding its applicability.

Findings

Roth's theorem successfully extended to finitely generated field extensions.

The use of Moriwaki's height framework enables this generalization.

Potential implications for Diophantine approximation over new fields.

Abstract

Roth's theorem is extended to finitely generated field extensions of $\Bbb Q$, using Moriwaki's framework for heights.