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On badly approximable numbers

Published 2 Feb 2020 in math.NT | (2002.00433v3)

Abstract: Motivated by a wonderful paper by Ngoc Ai Van Nguyen, Anthony Po\"els and Damien Roy, where a powerful method was introduced, we prove a criterion for a vector $\pmb{\alpha}\in \mathbb{R}d$ to be a badly approximable vector. Moreover we construct certain examples which show that a more general version of our criterion is not valid.

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