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Rad Hrvatske akademije znanosti i umjetnosti : Matematičke znanosti, No.532=21 Rujan 2017.

Izvorni znanstveni članak
https://doi.org/10.21857/mnlqgcj04y

Root separation for reducible monic polynomials of odd degree

Andrej Dujella   ORCID icon 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

Puni tekst: engleski, pdf (193 KB) str. 21-27 preuzimanja: 142* citiraj
APA 6th Edition
Dujella, A. i Pejković, T. (2017). Root separation for reducible monic polynomials of odd degree. Rad Hrvatske akademije znanosti i umjetnosti, (532=21), 21-27. https://doi.org/10.21857/mnlqgcj04y
MLA 8th Edition
Dujella, Andrej i Tomislav Pejković. "Root separation for reducible monic polynomials of odd degree." Rad Hrvatske akademije znanosti i umjetnosti, vol. , br. 532=21, 2017, str. 21-27. https://doi.org/10.21857/mnlqgcj04y. Citirano 16.12.2018.
Chicago 17th Edition
Dujella, Andrej i Tomislav Pejković. "Root separation for reducible monic polynomials of odd degree." Rad Hrvatske akademije znanosti i umjetnosti , br. 532=21 (2017): 21-27. https://doi.org/10.21857/mnlqgcj04y
Harvard
Dujella, A., i Pejković, T. (2017). 'Root separation for reducible monic polynomials of odd degree', Rad Hrvatske akademije znanosti i umjetnosti, (532=21), str. 21-27. doi: https://doi.org/10.21857/mnlqgcj04y
Vancouver
Dujella A, Pejković T. Root separation for reducible monic polynomials of odd degree. Rad Hrvatske akademije znanosti i umjetnosti [Internet]. 2017 [pristupljeno 16.12.2018.];(532=21):21-27. doi: https://doi.org/10.21857/mnlqgcj04y
IEEE
A. Dujella i T. Pejković, "Root separation for reducible monic polynomials of odd degree", Rad Hrvatske akademije znanosti i umjetnosti, vol., br. 532=21, str. 21-27, 2017. [Online]. doi: https://doi.org/10.21857/mnlqgcj04y

Sažetak
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}.

Ključne riječi
Integer polynomials; root separation

Projekti
HRZZ / IP / IP-2013-11-6422 / DIOPHANTINE - Diofantove m-torke, eliptičke krivulje, Thueove i indeksne jednadžbe

Hrčak ID: 186428

URI
https://hrcak.srce.hr/186428

Posjeta: 186 *