On the asymptotic behavior of Sudler products along subsequences

DOI10.1016/J.JMAA.2022.126841arXiv2103.14307MaRDI QIDQ6363807

Mario Neumüller

Publication date: 26 March 2021

Abstract: Let $alphain(0,1)$ and irrational. We investigate the asymptotic behaviour of sequences of certain trigonometric products (Sudler products) $(P_N(alpha){)}_{NinmathbbN}$ with ${\displaystyle }$P_N(alpha) =prod_{r=1}^N|2sin(pi r alpha)|.${\displaystyle }$ More precisely, we are interested in the asymptotic behaviour of subsequences of the form $(P_{q_n(alpha)}(alpha){)}_{ninmathbbN}$, where $q_n(alpha)$ is the $n$th best approximation denominator of $alpha$. Interesting upper and lower bounds for the growth of these subsequences are given, and convergence results, obtained by Mestel and Verschueren (see arXiv:1411.2252math[DS]) and Grepstad and Neum"uller (see arXiv:1801.09416[math.NT]), are generalized to the case of irrationals with bounded continued fraction coefficients.

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Continued fractions (11A55) Well-distributed sequences and other variations (11K36)

This page was built for publication: On the asymptotic behavior of Sudler products along subsequences

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6363807)