A Private Case of Sendov's Conjecture

Todor Stoyanov Stoyanov

Abstract

In this paper, we prove Sendov’s conjecture, when a polynomial is with real coefficients and the conjecture is relevant to the zeros, which belong to the set M = D (0, 1) ∩ [D (1, 1) ∪ D (−1, 1)]. We can see it in Figure 1. The conjecture is true for the filled areas.

Keywords

zeros, complex polynomial, real polynomial, disk, derivative, integral.

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