Root separation for reducible monic polynomials of odd degree
Number Theory
2017-09-19 v1
Abstract
We study root separation of reducible monic integer polynomials of odd degree. Let h(P) be the naive height, sep(P) the minimal distance between two distinct roots of an integer polynomial P(x) and sep(P)=h(P)^{-e(P)}. Let e_r*(d)=limsup_{deg(P)=d, h(P)-> +infty} e(P), where the limsup is taken over the reducible monic integer polynomials P(x) of degree d. We prove that e_r*(d) <= d-2. We also obtain a lower bound for e_r*(d) for d odd, which improves previously known lower bounds for e_r*(d) when d = 5, 7, 9.
Cite
@article{arxiv.1703.02120,
title = {Root separation for reducible monic polynomials of odd degree},
author = {Andrej Dujella and Tomislav Pejkovic},
journal= {arXiv preprint arXiv:1703.02120},
year = {2017}
}
Comments
8 pages, to appear in Rad Hrvat. Akad. Znan. Umjet. Mat. Znan