# Roth’s Theorem over arithmetic function fields

```@article{Vojta2021RothsTO,
title={Roth’s Theorem over arithmetic function
fields},
author={Paul Vojta},
journal={Algebra \& Number Theory},
year={2021}
}```
• Paul Vojta
• Published 28 June 2018
• Mathematics
• Algebra & Number Theory
Roth's theorem is extended to finitely generated field extensions of \$\Bbb Q\$, using Moriwaki's framework for heights.
2 Citations
On the generalisation of Roth's theorem
• Mathematics
• 2021
We present two possible generalisations of Roth’s approximation theorem on proper adelic curves, assuming some technical conditions on the behavior of the logarithmic absolute values. We illustrate
A generalised Roth’s theorem
• Mathematics
• 2021
0 Introduction 0.1 History The celebrated Roth’s theorem proved in [Rot55] asserts that the approximation exponent of a real algebraic number is 2. An equivalent, but more detailed statement is the

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