La Trobe

Metrical properties of Hurwitz continued fractions

journal contribution
posted on 2025-03-24, 04:23 authored by Yann Bugeaud, Gerardo RobertGerardo Robert, Mumtaz HussainMumtaz Hussain

We develop the geometry of Hurwitz continued fractions, a major tool in understanding the approximation properties of complex numbers by ratios of Gaussian integers. Based on a thorough study of the geometric properties of Hurwitz continued fractions, among other things, we determine that the space of valid sequences is not a closed set of sequences. Additionally, we establish a comprehensive metrical theory for Hurwitz continued fractions.

History

Publication Date

2025-05-01

Journal

Advances in Mathematics

Volume

468

Article Number

110208

Pagination

94p.

Publisher

Elsevier

ISSN

0001-8708

Rights Statement

© 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Usage metrics

    Journal Articles

    Licence

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC