Some theorems on generalized polars with arbitrary weight (Q579453)

The authors continue their study [Ann. Mat. Pura Appl., IV. Ser. 126, 363-377 (1980; Zbl 0455.30007)] of generalized polars of abstract homogeneous polynomials, introduced by \textit{M. Marden} [SIAM J. Numer. Anal. 3, 269-275 (1966; Zbl 0173.027)]. Their main result gives sufficient conditions for the non-vanishing of such polars. As an application the authors obtain a generalization of a result of \textit{J. L. Walsh} [Trans. Am. Math. Soc. 22, 101-116 (1921)] concerning critical points of complex rational functions.