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