Sendov's conjecture

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Sendov's conjecture

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Named after Bulgarian mathematician Blagovest Sendov.

(mathematics) 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 $f(z)=(z-r_{1})\cdots (z-r_{n}),\qquad (n\geq 2)$ 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.
Synonym: Ilieff's conjecture

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English Wikipedia has an article on:

Sendov's conjecture

Wikipedia

Named after Bulgarian mathematician Blagovest Sendov.

(mathematics) 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 $f(z)=(z-r_{1})\cdots (z-r_{n}),\qquad (n\geq 2)$ 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.
Synonym: Ilieff's conjecture

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