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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...
[Sendov Bl.; Sendov Blagovest; Sendow Bl.; Сендов Благовест]
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