On the generalisation of Roth's theorem

Paolo Dolce; Francesco Zucconi

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arXiv · 2111.12409

On the generalisation of Roth's theorem

Paolo Dolce·Francesco Zucconi

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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.

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Paolo Dolce, Francesco Zucconi. 2021-11-24. On the generalisation of Roth's theorem. https://arxiv.org/abs/2111.12409

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