Naslov
Polynomial root separation

Autori
Dujella, Andrej

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

Izvornik
23rd Czech and Slovak International Conference on Number Theory / - Ostrava : University of Ostrava, 2017, 15-15

Skup
23rd Czech and Slovak International Conference on Number Theory

Mjesto i datum
Ostravice, Češka Republika, 28.08.2017. - 01.09.2017

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Polynomial, root separation

Sažetak
We consider the question how close to each other can be two distinct roots of an integer polynomial P(X) of degree d. We compare the distance between two distinct roots of P(X) with its height H(P), defined as the maximum of the absolute values of its coefficients. The first result in this direction in due to Mahler, who proved that the distance is > c(d)H(P) −d+1, for an explicit constant c(d), depending only on d. We will present some results in the opposite direction, obtained by constructing explicit parametric families of polynomials having two roots very close to each other. We also consider the absolute variant of the problem (the minimal nonzero distance between absolute values of the roots), and give tight bounds for the case of real roots. This is a joint work with Yann Bugeaud, Tomislav Pejković and Bruno Salvy.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA