Work

Rational Approximation With Chosen Numerators

Year: 2025

Type: article

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.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnaf355

Authors: Manuel Hauke, Emmanuel Kowalski

Institutions: Norwegian University of Science and Technology, Graz University of Technology, ETH Zurich

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,534

Funders: Eidgenössische Technische Hochschule Zürich, Vetenskapsrådet