Statistically characterized subgroups of the circle (II): continued fractions

DOI10.1016/J.BULSCI.2022.103174arXiv2011.03786MaRDI QIDQ6353214

Pratulananda Das, Kumardipta Bose

Publication date: 7 November 2020

Abstract: In this note, we continue the investigation of the new version of characterized subgroups of the circle group $mathbbT$, namely, "statistically characterized subgroups" (shortly, "s-characterized subgroups") recently introduced in cite{DDB}. We primarily investigate these subgroups for sequences arising out of continued fraction representation of irrational numbers $alpha$ in line of cite{L} and cite{KL} (followed by cite{BDMW1}) comparing their main results for this new notion and show that these subgroups are strictly larger in size (so nontrivial) than the corresponding characterized subgroups, having cardinality $mathfrakc$ and containing the subgroup $langlealphaangle$ and in the process answer the Open Question 6.4 posed in cite{DDB}.

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Continued fractions and generalizations (11J70) General properties and structure of LCA groups (22B05)

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