Probabilities for absolute irreducibility of multivariate polynomials by the polytope method

Abstract

Motivated by the Dubickas's result in [1], which computes the probability of the irreducible polynomials by Eisenstein's criterion for some families of polynomials in Z[x], we calculate the probabilities which represent the ratio of absolutely irreducible multivariate polynomials by the polytope method in some families of polynomials over arbitrary fields.