Convergence rate for R\'enyi-type continued fraction expansions
Number Theory
2018-10-26 v2
Abstract
This paper continues our investigation of Renyi-type continued fractions studied in \cite{Sebe&Lascu-2018}. A Wirsing-type approach to the Perron-Frobenius operator of the R\'enyi-type continued fraction transformation under its invariant measure allows us to study the optimality of the convergence rate. Actually, we obtain upper and lower bounds of the convergence rate which provide a near-optimal solution to the Gauss-Kuzmin-L\'evy problem.
Keywords
Cite
@article{arxiv.1810.10248,
title = {Convergence rate for R\'enyi-type continued fraction expansions},
author = {Gabriela Ileana Sebe and Dan Lascu},
journal= {arXiv preprint arXiv:1810.10248},
year = {2018}
}
Comments
14 pages