Metrical properties of Hurwitz continued fractions
<p dir="ltr">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.
Authors
- Gerardo González Robert (ORCID: https://orcid.org/0000-0001-8792-967X)
- Mumtaz Hussain (ORCID: https://orcid.org/0000-0001-5621-9341)
- Yann Bugeaud (ORCID: https://orcid.org/0000-0002-8621-5699)
Publication Details
- Journal
- Advances in Mathematics
- Published
- 2025-03-18
- DOI
- https://doi.org/10.1016/j.aim.2025.110208
- Citations
- 6
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 22.15
Funders
- Agence Nationale de la Recherche
- Consejo Nacional de Ciencia y Tecnología
- Australian Research Council