Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica (Dec 2014)
Irreducibility Criteria for Compositions and Multiplicative Convolutions of Polynomials with Integer Coefficients
Abstract
We provide irreducibility criteria for multiplicative convolutions of polynomials with integer coefficients, that is, for polynomials of the form hdeg 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 hdeg 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.
Keywords