Root separation for irreducible integer polynomials

TL;DR

This paper presents improved bounds on the separation of roots for irreducible integer polynomials of degree four or higher, advancing previous theoretical results in algebraic number theory.

Contribution

It provides new, tighter bounds on root separation for irreducible integer polynomials, extending and refining earlier theoretical bounds.

Findings

Improved root separation bounds for even degree polynomials

Enhanced bounds for odd degree polynomials

Advances in algebraic number theory related to polynomial roots

Abstract

We establish new results on root separation of integer, irreducible polynomials of degree at least four. These improve earlier bounds of Bugeaud and Mignotte (for even degree) and of Beresnevich, Bernik, and Goetze (for odd degree).