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
Publication date:
13.9.2017.
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