Sendov's conjecture

== English == === Etymology === Named after Bulgarian mathematician Blagovest Sendov. === Proper noun === Sendov's conjecture (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 ) ⋯ ( z − r n ) , ( n ≥ 2 ) {\displaystyle f(z)=(z-r_{1})\cdots (z-r_{n}),\qquad (n\geq 2)} with all roots r1, ..., rn 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