A note on the Ilyeff-Sendov conjecture (Q803316)

The author gives a proof of the Ilieff-Sendov conjecture for arbitrary polynomials with four distinct zeros. This result extends the analogous theorem for three distinct zeros by \textit{E. B. Saff} and \textit{J. B. Twomey} [Proc. Am. Math. Soc. 27, 303-308 (1971; Zbl 0218.30002)]. In this case however a similar result for a polynomial of \[ a_ 0z^{n_ 0}+a_ 1z^{n_ 1}+a_ 2z^{n_ 2} \] was proved by \textit{G. Schmeißer} [Rend. Semin. Math. Univ. Padova 46, 405-415 (1971)].