Rational Approximation With Chosen Numerators
Abstract We consider the problem of approaching real numbers with rational numbers with prime denominator and with a single numerator allowed for each denominator. We obtain basic results, both probabilistic and deterministic, draw connections to twisted diophantine approximation, and present a simple application, related to possible correlations between trace functions and dynamical sequences.
Authors
- Manuel Hauke (ORCID: https://orcid.org/0000-0002-6244-0285)
- Emmanuel Kowalski (ORCID: https://orcid.org/0009-0009-8487-8729)
Institutions
- ETH Zurich (CH)
- Graz University of Technology (AT)
- NTNU Samfunnsforskning (NO)
Publication Details
- Journal
- International Mathematics Research Notices
- Published
- 2025-11-21
- DOI
- https://doi.org/10.1093/imrn/rnaf355
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Eidgenössische Technische Hochschule Zürich
- Vetenskapsrådet