Springer Online Journal Archives 1860-2000
Summary The present paper deals with certain new aspects of the theory of algebra-valued generalized polars of the product of abstract homogeneous polynomials, opening up new avenues to the existing (and still very young) theory put forward by Marden and Zaheer (see Pacific J. Math., 74 (1978), n. 2, pp. 535–557). Our main theorem here leads, on the one hand, to an improved version of Walsh's cross-ratio theorem on critical points of functions of the formf 1 f 2/f 3 (f i being complex-valued polynomials) and, on the other hand, it offers a two-fold generalization of one of the main theorems of Zaheer in the paper cited above.
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