English

On the number of primes for which a polynomial is Eisenstein

Number Theory 2019-01-28 v1

Abstract

Previously Heyman and Shparlinski gave an asymptotic formula with error term for the number of Eisenstein polynomials of fixed degree and bounded height. Let ψ(f)\psi(f) denote the number of primes for which a polynomial ff is Eisenstein. We give expressions for the mean and variance of the function ψ\psi for each fixed degree, where the polynomials are ordered according to their height.

Keywords

Cite

@article{arxiv.1901.09014,
  title  = {On the number of primes for which a polynomial is Eisenstein},
  author = {Shilin Ma and Kevin McGown and Devon Rhodes and Mathias Wanner},
  journal= {arXiv preprint arXiv:1901.09014},
  year   = {2019}
}