English

On the distribution of reducible polynomials

Number Theory 2020-08-14 v1 Rings and Algebras

Abstract

Let Y_n(t) denote the set of all polynomials over the ring Z which are reducible over the field Q and of degree n>1 and of height not greater than t. We show that the true order of magnitude of |Y_n(t)| equals t^2 log t in the special case n=2 and it equals t^n for each n>2. We also determine the true order of magnitude of the size of certain interesting subsets of Y_n(t).

Keywords

Cite

@article{arxiv.2008.05815,
  title  = {On the distribution of reducible polynomials},
  author = {Gerald Kuba},
  journal= {arXiv preprint arXiv:2008.05815},
  year   = {2020}
}