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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A remark on the set of exactly approximable vectors in the simultaneous case
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by Reynold Fregoli;
Proc. Amer. Math. Soc. 152 (2024), 3177-3182
DOI: https://doi.org/10.1090/proc/16790
Published electronically: June 14, 2024

Abstract:

We compute the Hausdorff dimension of the set of $\psi$-exactly approximable vectors, in the simultaneous case, in dimension strictly larger than $2$ and for approximating functions $\psi$ with order at infinity less than or equal to $-2$. Our method relies on the analogous result in dimension $1$, proved by Yann Bugeaud and Carlos Moreira, and a version of Jarník’s theorem on fibres.
References
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Bibliographic Information
  • Reynold Fregoli
  • Affiliation: Department of Mathematics, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
  • Address at time of publication: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
  • MR Author ID: 1318722
  • Email: reynoldfregoli@gmail.com
  • Received by editor(s): April 5, 2023
  • Received by editor(s) in revised form: December 20, 2023, and January 6, 2024
  • Published electronically: June 14, 2024
  • Additional Notes: The author was supported by SNSF grant 200021–182089.
  • Communicated by: Rachel Pries
  • © Copyright 2024 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 3177-3182
  • MSC (2020): Primary 11J13, 11J83
  • DOI: https://doi.org/10.1090/proc/16790
  • MathSciNet review: 4767253