Superoptimal continued fractions

Proceedings of the American Mathematical Society 2026

View at publisher
Authors: Slade Sanderson
DOI: 10.1090/proc/17626
Cited by: 0
References: 14

Abstract

Motivated by the optimal continued fractions studied independently by Selenius [Acta Acad. Aboensis 22 (1960), 77 pp.] and Bosma [Nederl. Akad. Wetensch. Indag. Math. 49 (1987), pp. 353–379], we define and introduce algorithms producing superoptimal continued fraction expansions of irrationals. The convergents of these expansions simultaneously provide arbitrarily good rational approximations and converge arbitrarily quickly.

Fields of Study & Subjects

Analytic Number Theory Research Mathematical functions and polynomials Mathematical Dynamics and Fractals

Publication details

Journal / source
Proceedings of the American Mathematical Society
Volume
154
Issue
8
Pages
3219–3237
Publication date
14 January 2026
Language
EN