Sendov's conjecture

English

Etymology

Named after Bulgarian mathematician Template:W.

Proper noun

1. 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 $f(z)=(z-r_1)\cdots (z-r_n),(n\ge 2)$ 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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