On a problem of Gauss-Kuzmin type for continued fraction with odd partial quotients

Sofia Kalpazidou

Vol. 123 (1986), No. 1, 103–114

DOI: 10.2140/pjm.1986.123.103

Abstract

Let x be a number of the unit interval. Then x may be written in a unique way as a continued fraction

where 𝜖_n ∈{−1,1}, α_n ≥ 1, α_n ≡ 1 (mod 2) and α_n + 𝜖_n > 1. Using the ergodic behaviour of a certain homogeneous random system with complete connections we solve a variant of Gauss-Kuzmin problem for the above expansion.

Mathematical Subject Classification 2000

Primary: 11K50

Secondary: 11A55, 60K99

Milestones

Received: 5 October 1984

Published: 1 May 1986