Summary: We study integer coefficient polynomials of fixed degree and maximum height $H$ that are irreducible by the Dumas criterion. We call such polynomials Dumas polynomials. We derive upper bounds on the number of Dumas polynomials as $H \to \infty $. We also show that, for a fixed degree, the density of Dumas polynomials in the set of all irreducible integer coefficient polynomials is strictly less than 1.

11R09

irreducible polynomial, dumas criterion, coprimality