Continued fractions with minimal remainders
Elena Zhabitskaya
TL;DR
This paper investigates a special form of continued fractions related to the centered Euclidean algorithm, deriving a new formula for the limit distribution of sequences of rationals with bounded partial quotients.
Contribution
It introduces a novel formula for the limit distribution function of rational sequences with bounded partial quotients, linked to the centered Euclidean algorithm.
Findings
Derived a new formula for the limit distribution function.
Analyzed sequences of rationals with bounded sum of partial quotients.
Connected continued fractions to the centered Euclidean algorithm.
Abstract
Consider the representation of a rational number in the form, associated with "centered" Euclidean algorithm. We prove a new formula for the limit distribution function for sequences of rationals with bounded sum of partial quotients.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Combinatorial Mathematics · Advanced Mathematical Identities