Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899434 | Journal of Mathematical Analysis and Applications | 2018 | 33 Pages |
Abstract
We study the asymptotic behaviour of the sequence of sine products Pn(α)=âr=1n|2sinâ¡Ïrα| for real quadratic irrationals α. In particular, we study the subsequence Qn(α)=âr=1qn|2sinâ¡Ïrα|, where qn is the nth best approximation denominator of α, and show that this subsequence converges to a periodic sequence whose period equals that of the continued fraction expansion of α. This verifies a conjecture recently posed by Verschueren and Mestel (2016) [15].
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Sigrid Grepstad, Mario Neumüller,