The generalised Hausdorff measure of sets of Dirichlet non-improvable numbers

The generalised Hausdorff measure of sets of Dirichlet non-improvable numbers

Let \psi :\mathbb {R}_+\to \mathbb {R}_+ be a non-increasing function. A real number x is said to be \psi-Dirichlet improvable if the system \begin{equation*} |qx-p|< \psi (t) \ \ {\text {and}} \ \ |q|

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Veröffentlicht in:Proceedings of the American Mathematical Society 2023-05, Vol.151 (5), p.1823
Hauptverfasser: Bos, Philip, Hussain, Mumtaz, Simmons, David
Format: Artikel
Sprache:eng
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Zusammenfassung:Let \psi :\mathbb {R}_+\to \mathbb {R}_+ be a non-increasing function. A real number x is said to be \psi-Dirichlet improvable if the system \begin{equation*} |qx-p|< \psi (t) \ \ {\text {and}} \ \ |q|
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/16222