Original scientific paper

https://doi.org/10.21857/mnlqgcj04y

Root separation for reducible monic polynomials of odd degree

Andrej Dujella orcid.org/0000-0001-6867-5811 ; Department of Mathematics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia
Tomislav Pejković ; Department of Mathematics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia

Abstract

We study root separation of reducible monic integer polynomials of odd degree. Let H(P) be the naïve 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) = lim sup_{deg(P)=d, H(P)→+∞} e(P), where the lim sup 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}.

Keywords

Integer polynomials; root separation

Hrčak ID:

186428

URI

https://hrcak.srce.hr/186428

Publication date:

13.9.2017.

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