English

The Density of Shifted and Affine Eisenstein Polynomials

Number Theory 2019-02-13 v1

Abstract

In this paper we provide a complete answer to a question by Heyman and Shparlinski concerning the natural density of polynomials which are irreducible by Eisenstein's criterion after applying some shift. The main tool we use is a local to global principle for density computations over a free Z\mathbb Z-module of finite rank.

Keywords

Cite

@article{arxiv.1507.02753,
  title  = {The Density of Shifted and Affine Eisenstein Polynomials},
  author = {Giacomo Micheli and Reto Schnyder},
  journal= {arXiv preprint arXiv:1507.02753},
  year   = {2019}
}