English

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

R2 v1 2026-06-24T07:50:19.413Z