Sendov's conjecture

Ní ìmọ̀ ìṣirò, Sendov's conjecture, nígbàmíràn wọ́n má a ń pèé ní Ilieff's conjecture, nííṣe pẹ̀lú ibi tí àwọn root àti àwọn ojú ibi iṣẹ́ polynomial ti complex variable. Wọ́n sọọ́ lórúkọ Blagovest Sendov.

Conjection yìí sọ pé fún polynomial

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

pẹ̀lú gbogbo àwọn  r₁, ..., r_n inú unit disk |z| ≤ 1, ìkànkan àwọn n root tí ìjìnasí wọn kò ju ẹyọ kan lati ojú kan.

Àwọn ìtọ́kasí

• G. Schmeisser, "The Conjectures of Sendov and Smale," Approximation Theory: A Volume Dedicated to Blagovest Sendov (B. Bojoanov, ed.), Sofia: DARBA, 2002 pp. 353–369.

Àwọn ìjápọ̀ látìta

• Sendov's Conjecture by Bruce Torrence with contributions from Paul Abbott at The Wolfram Demonstrations Project