Geodesic
Some remarks on rotation theorems for complex polynomials
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 369-376

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For any complex polynomial $P(z)=c_0+c_1z+...+c_nz^n, c_n\not=0,$ having all its zeros in the unit disk $|z|\le 1,$ we consider the behavior of the function (arg$P(e^{i\theta}))'_{\theta}$ when the real argument $\theta$ changes. We give some sharp estimates of this function involving of the values of $P(e^{i\theta}),$ arg$P(e^{i\theta})$ or the coefficients $c_k, k=0,1,n-1,n.$
Keywords: complex polynomials, rotation theorems, inequalities, boundary Schwarz lemma, rational functions. 
V. N. Dubinin. Some remarks on rotation theorems for complex polynomials. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 369-376. http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a44/
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