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 → ∞. 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.
|Number of pages||7|
|Journal||Journal of Integer Sequences|
|Publication status||Published - 2014|
- Dumas criterion
- Irreducible polynomial