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Badly Approximable Matrices and Diophantine Exponents

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Abstract

This paper is a survey of results concerning different kinds of Diophantine exponents. Special attention is paid to the transference principle and the generalization of the concept of badly approximable numbers to matrices and lattices.

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ACKNOWLEDGMENTS

The author is a winner of the “Junior Leader” contest conducted by the Theoretical Physics and Mathematics Advancement Foundation “BASIS” and would like to thank its sponsors and jury.

Funding

This work was supported by the Russian Science Foundation, grant no. 22-41-05001, https://rscf.ru/project/22-41-05001/.

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    O. N. German

  2. Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia

    O. N. German

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  1. O. N. German
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Correspondence to O. N. German.

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The author declares that he has no conflicts of interest.

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Translated by I. Ruzanova

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German, O.N. Badly Approximable Matrices and Diophantine Exponents. Dokl. Math. 106 (Suppl 2), S201–S220 (2022). https://doi.org/10.1134/S106456242270017X

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