Naslov
Root separation for reducible monic quartics

Autori
Pejković, Tomislav ; Dujella, Andrej

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Fifteenth International Conference on Fibonacci Numbers and Their Applications / Liptai, Kalman - Eger : Eszterhazy Karoly College, 2012, 39-39

Skup
Fifteenth International Conference on Fibonacci Numbers and Their Applications

Mjesto i datum
Eger, Mađarska, 25.06.2012. - 30.06.2012

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
root separation ; integer polynomials

Sažetak
We study root separation for reducible monic integer polynomials of degree four. Let H(P) be the height and sep(P) the minimal distance between two distinct roots of a separable integer polynomial P(x), and sep(P) = H(P)^{; ; -e(P)}; ; . We show that lim sup e(P) = 2, where limsup is taken over all reducible monic integer polynomials P(x) of degree 4. One part of our proof relies on the construction of a family of polynomials with very close roots. Coefficients in these polynomials are constructed using Fibonacci sequence. We also examine the case of families of polynomials which have polynomial and not exponential growth of coefficients.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA