English

On badly approximable numbers

Number Theory 2021-11-16 v3

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 αRd\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.

Cite

@article{arxiv.2002.00433,
  title  = {On badly approximable numbers},
  author = {Renat Akhunzhanov and Nikolay Moshchevitin},
  journal= {arXiv preprint arXiv:2002.00433},
  year   = {2021}
}

Comments

minor correction after refereeing

R2 v1 2026-06-23T13:28:16.671Z