Restricted simultaneous Diophantine approximation

TL;DR

This paper investigates the problem of approximating points on lines in multi-dimensional space using Diophantine methods, with added constraints related to primality conditions.

Contribution

It introduces a novel approach to Diophantine approximation on lines considering primality restrictions, expanding the scope of classical approximation problems.

Findings

Established bounds for approximation under primality constraints

Extended classical Diophantine results to primality-restricted settings

Provided new insights into the distribution of prime-related approximations

Abstract

We study the problem of Diophantine approximation on lines in $\mathbb{R}^d$ under certain primality restrictions.