Sendov's conjecture

English

Named after Bulgarian mathematician Template:W.

Template:Lb A conjecture concerning the relationship between the locations of roots and critical points of a polynomial function of a complex variable. It states that for a polynomial $f (z) = (z - r_{1}) \dots (z - r_{n}), (n \geq 2)$ with all roots r₁, ..., r_n inside the closed unit disk |z| ≤ 1, each of the n roots is at a distance no more than 1 from at least one critical point.
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