On the generalisation of Roth's theorem
Number Theory
2023-05-16 v4
Abstract
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 how tightening such assumptions makes our inequalities stronger. As special cases we recover Corvaja's results [Cor97] for fields admitting a product formula, and Vojta's ones [Voj21] for arithmetic function fields.
Keywords
Cite
@article{arxiv.2111.12409,
title = {On the generalisation of Roth's theorem},
author = {Paolo Dolce and Francesco Zucconi},
journal= {arXiv preprint arXiv:2111.12409},
year = {2023}
}
Comments
Typos fixed