Hausdorffsche Metrik und Approximationen.
Generalization of a Conjecture in the Geometry of Polynomials
In this paper we survey work on and around the following conjecture, which was first stated about 45 years ago: If all the zeros of an algebraic polynomial p (of degree n ≥ 2) lie in a disk with radius r, then, for each zero z1 of p, the disk with center z1 and radius r contains at least one zero of the derivative p′ . Until now, this conjecture has been proved for n ≤ 8 only. We also put the conjecture in a more general framework involving higher order derivatives and sets defined by the zeros...
Ljubomir Iliev – Leader of The Bulgarian Mathematical Community (in the Occasion of His Centenary)
[Sendov Bl.; Sendov Blagovest; Sendow Bl.; Сендов Благовест]
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