Irreducibility Criteria for Compositions and Multiplicative Convolutions of Polynomials with Integer Coefficients
Anca Iuliana Bonciocat, Nicolae Ciprian Bonciocat, Mihai Cipu · Analele Universităţii "Ovidius" Constanţa. Seria Matematică · 2014
Abstract We provide irreducibility criteria for multiplicative convolutions of polynomials with integer coefficients, that is, for polynomials of the form h deg f · f(g/h) , where f, g, h are polynomials with integer coefficients, and g and h are relatively prime. The irreducibility conditions are expressed in terms of the prime factorization of the leading coefficient of the polynomial h deg f · f(g/h) , the degrees of f, g, h , and the absolute values of their coefficients. In particular, by letting h = 1 we obtain irreducibility conditions for compositions of polynomials with integer coefficients.