Naslov
Root separation for reducible integer polynomials

Autori
Dujella, Andrej ; Bugeaud, Yann

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

Izvornik
The Geometry, Algebra and Analysis of Algebraic Numbers / - Banff, 2015, 5-5

Skup
The Geometry, Algebra and Analysis of Algebraic Numbers

Mjesto i datum
Banff, Kanada, 04.10.2015. - 09.10.2015

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
root separation; integer polynomials

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 recent results in the opposite direction, obtained by constructing explicit parametric families of (monic) reducible polynomials having two roots very close to each other.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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