Approximated solution of a differential-difference equation arising in number theory and applications to the linear sieve

TL;DR

This paper presents elementary and precise numerical solutions to a differential-difference equation related to number theory, enhancing the explicit linear sieve method introduced by Nathanson.

Contribution

It offers improved numerical methods for solving a key differential-difference equation in number theory, advancing the linear sieve technique.

Findings

More accurate numerical solutions achieved

Enhanced explicit linear sieve implementation

Potential applications in prime number theory

Abstract

We provide elementary and accurate numerical solutions to the differential-difference equation, which improves an explicit version of the linear sieve given by Nathanson.