2016/10/11 by David Krumm, Krumm, David
Computer Science · Mathematics · #Algebraic structures and combinatorial models #Complexity and Algorithms in Graphs #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1610.03528
openalex publication_date 2016/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let P(T,X) be an irreducible polynomial in two variables with rational coefficients. It follows from Hilbert's Irreducibility Theorem that for most rational numbers t the specialized polynomial P(t,X) is irreducible and has the same Galois group as P. We discuss here a method for obtaining an explicit description of the set of exceptional numbers t, i.e., those for which P(t,X) is either reducible or has a different Galois group than P. To illustrate the method we determine the exceptional specializations of two polynomials of degrees four and six.