Root separation for integer polynomials (CROSBI ID 622633)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa
Podaci o odgovornosti
Dujella, Andrej
engleski
Root separation for integer polynomials
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 maximal 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 opposite direction, obtained by constructing explicit families of irreducible and reducible polynomials of degree d whose roots are very close. This is joint work with Yann Bugeaud.
polynomials; root separation
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Podaci o prilogu
1-1.
2014.
objavljeno
Podaci o matičnoj publikaciji
Representations of p-adic groups
Podaci o skupu
Representations of p-adic groups ; A conference dedicated to Marko Tadic on his 60th birthday
pozvano predavanje
16.06.2014-20.06.2014
Zagreb, Hrvatska