English

On the Number of Eisenstein Polynomials of Bounded Height

Number Theory 2017-07-12 v1

Abstract

We obtain a more precise version of an asymptotic formula of A. Dubickas for the number of monic Eisenstein polynomials of fixed degree dd and of height at most HH, as HH\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 HH.

Keywords

Cite

@article{arxiv.1302.6094,
  title  = {On the Number of Eisenstein Polynomials of Bounded Height},
  author = {Randell Heyman and Igor E. Shparlinski},
  journal= {arXiv preprint arXiv:1302.6094},
  year   = {2017}
}