Some metric properties of \(\alpha\)-continued fractions.
Borel-Bernstein theorem is one of the metrical theorems on the partial quotients of the regular continued fractions. There are also some almost everywhere properties, which were shown by \textit{H, G. Diamond} and \textit{J. D. Vaaler} [Pac. J. Math. 122, 73--82 (1986; Zbl 0589.10056)] or by \textit{W. Philipp} [Acta Arith. 28, 379--386 (1976; Zbl 0332.10033)]. In this paper, the authors show that these metrical properties also hold for any \(\alpha\)-continued fraction for \(1/2\leq\alpha<1\). It is a modification of the nearest integer continued fractions taking \(n\) as the integer part of \(y\) when \(y\in[n-1+\alpha,n+\alpha)\) for \(1/2\leq\alpha\leq 1\), instead of the nearest integer.
Maxima of continued fraction coefficients
scientific article; zbMATH DE number 1891443