Root separation for reducible monic polynomials of odd degree (CROSBI ID 237132)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Dujella, Andrej ; Pejković, Tomislav
engleski
Root separation for reducible monic polynomials of odd degree
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)→+∞}; ; ; ; ; 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}; ; ; ; ; .
integer polynomials, root separation
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
Podaci o izdanju
21
2017.
21-27
objavljeno
1845-4100
1849-2215
10.21857/mnlqgcj04y
Povezanost rada
Matematika