Sendov's conjecture

Named after Bulgarian mathematician Blagovest Sendov.

Sendov's conjecture

1. (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 ${\displaystyle f(z)=(z-r_{1})\cdots (z-r_{n}),\qquad (n\geq 2)}$ 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