Geodesic
On the number of polynomials of bounded height that satisfy the Dumas criterion
Journal of integer sequences, Tome 17 (2014) no. 2.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
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},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_2_a3/}
}
TY  - JOUR
AU  - Heyman, Randell
TI  - On the number of polynomials of bounded height that satisfy the Dumas criterion
JO  - Journal of integer sequences
PY  - 2014
VL  - 17
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JIS_2014__17_2_a3/
LA  - en
ID  - JIS_2014__17_2_a3
ER  - 
%0 Journal Article
%A Heyman, Randell
%T On the number of polynomials of bounded height that satisfy the Dumas criterion
%J Journal of integer sequences
%D 2014
%V 17
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JIS_2014__17_2_a3/
%G en
%F JIS_2014__17_2_a3
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/