Metric properties of Oppenheim continued fractions in the field of Laurent series

Abstract

Let (Figure presented.) be the field of Laurent series over the finite field (Figure presented.) complete with respect to the degree valuation |·| and let I denote the ring (Figure presented.). It is known that there is a probability measure P with respect to the Haar measure on (Figure presented.) normalized by P(I) = 1. The aim of this work is to study some metric properties involving the sets of digits appeared in the Oppenheim continued fraction expansions of the Laurent series, using the measure P. © 2022 Taru Publications.