Irreducibility via location of zeros

TL;DR

This paper introduces new classes of irreducible polynomials with integer coefficients, characterized by the location of their zeros in the complex plane, using Perron-type conditions to establish irreducibility.

Contribution

It provides novel criteria for irreducibility based on the zeros' locations, expanding the understanding of polynomial irreducibility in relation to complex zeros.

Findings

New classes of irreducible polynomials with zeros inside specific regions

Perron-type conditions effectively determine irreducibility

Polynomials with zeros outside a closed annular region are also characterized

Abstract

In this paper, we obtain several new classes of irreducible polynomials having integer coefficients whose zeros lie inside an open disk around the origin or outside a closed annular region in the complex plane. Such irreducible polynomials are devised by imposing Perron--type sufficiency conditions on their coefficients.