On the Number of Eisenstein Polynomials of Bounded Height

Randell Heyman, Igor E. Shparlinski

Published 2013-02-25Version 1

We obtain a more precise version of an asymptotic formula of A. Dubickas for the number of monic Eisenstein polynomials of fixed degree $d$ and of height at most $H$, as $H\to \infty$. In particular, we give an explicit bound for the error term. We also obtain an asymptotic formula for arbitrary Eisenstein polynomials of height at most $H$.