On the Number of Polynomials of Bounded Height that Satisfy the Dumas Criterion
Randell Heyman
Department of Computing
Macquarie University
Sydney, NSW 2109
Australia
Abstract:
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.
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Received June 3 2013;
revised version received December 12 2013;
Published in Journal of Integer Sequences, January 4 2014.
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