Abstract
Motivated by a wonderful paper [7] where a powerful method was introduced, we prove a criterion for a vector \(\varvec{\alpha }\in {\mathbb {R}}^d\) 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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Notes
It is important that the constants in (70) do not depend on \(\gamma _1\).
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Acknowledgements
The authors thank the anonymous referee for careful reading of the manuscript and for important suggestions. The second named is a winner of the “Leader” contest conducted by Theoretical Physics and Mathematics Advancement Foundation “BASIS” and would like to thank the foundation and jury.
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Research is supported by the Russian Science Foundation under grant 19-11-00001.
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Akhunzhanov, R., Moshchevitin, N. On badly approximable vectors. Math. Z. 301, 1573–1602 (2022). https://doi.org/10.1007/s00209-021-02939-9
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DOI: https://doi.org/10.1007/s00209-021-02939-9