Rational approximation with chosen numerators
Number Theory
2025-11-21 v3 Dynamical Systems
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.
Cite
@article{arxiv.2502.08335,
title = {Rational approximation with chosen numerators},
author = {Manuel Hauke and Emmanuel Kowalski},
journal= {arXiv preprint arXiv:2502.08335},
year = {2025}
}
Comments
27 pages; to appear in IMRN; changed minor typographical mistakes and added some remarks