Metric theorems for continued β-fractions

• Published in: Monatshefte für Mathematik Vol. 190; no. 2; pp. 281 - 299
• Main Authors: Feng, Jing, Ma, Chao, Wang, Shuailing
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01.10.2019; Springer Nature B.V
• Subjects: Divergence; Mathematics; Mathematics and Statistics; Polynomials; Quotients; Integers; Partial quotients; 28A80; 11K55; Continued; fractions

Let β > 1 be a root of the polynomial t 2 = a t + 1 with a ∈ N , a ≥ 1 or a root of the polynomial t 2 = a t - 1 with a ∈ N , a ≥ 3 . In this paper, we consider the metric properties of the continued β -fractions. We show that the Lebesgue measure of the following set E ( φ ) = { x ∈ [ 0 , 1 ) :...