A near-optimal solution to the Gauss-Kuzmin-Levy problem for θ-expansions

JOURNAL OF NUMBER THEORY

卷:171

Article

Sebe, Gabriela Ileana^1,2 

[1] Univ Politehn Bucuresti, Fac Sci Appl, Splaiul Independentei 313, Bucharest 060042, Romania

[2] Inst Math Stat & Appl Math, Calea 13 Septembrie 13, Bucharest 050711, Romania

关键词: theta-expansions;    Invariant measure;    Gauss-Kuzmin-Levy problem;    Perron-Frobenius operator;   

DOI  :  10.1016/j.jnt.2016.07.003

来源: Elsevier

【 摘 要 】

Chakraborty and Rao [4] considered the theta-expansions of numbers in [0,theta), where 0 < theta < 1. A Wirsing-type approach to the Perron-Frobenius operator of the generalized Gauss map 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-Levy problem. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free