Geodesic
On the number of polynomials of bounded height that satisfy the Dumas criterion
Journal of integer sequences, Tome 17 (2014) no. 2
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.
Classification : 11R09
Keywords: irreducible polynomial, dumas criterion, coprimality 
@article{JIS_2014__17_2_a3,
     author = {Heyman,  Randell},
     title = {On the number of polynomials of bounded height that satisfy the {Dumas} criterion},
     journal = {Journal of integer sequences},
     year = {2014},
     volume = {17},
     number = {2},
     zbl = {1285.11132},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_2_a3/}
}
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Heyman,  Randell. On the number of polynomials of bounded height that satisfy the Dumas criterion. Journal of integer sequences, Tome 17 (2014) no. 2. http://geodesic.mathdoc.fr/item/JIS_2014__17_2_a3/