Continued fractions with odd partial quotients
Elena Zhabitskaya
TL;DR
This paper investigates the limit distribution of sequences of rational numbers with bounded sum of partial quotients, using continued fractions associated with the odd Euclidean algorithm, and proves specific properties of this distribution.
Contribution
It introduces new properties of the limit distribution function for rationals with bounded partial quotients in the context of odd continued fractions.
Findings
Established properties of the limit distribution function.
Analyzed sequences of rationals with bounded sum of partial quotients.
Connected continued fractions with the odd Euclidean algorithm to distribution properties.
Abstract
Consider the representation of a rational number as a continued fraction, associated with "odd" Euclidean algorithm. In this paper we prove certain properties for the limit distribution function for sequences of rationals with bounded sum of partial quotients
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