Geodesic
Distortion theorems for polynomials on a circle
Sbornik. Mathematics, Tome 191 (2000) no. 12, pp. 1797-1807 Cet article a éte moissonné depuis la source Math-Net.Ru

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Inequalities for the derivatives with respect to $\varphi=\arg z$ the functions $\operatorname{Re}P(z)$, $|P(z)|^2$ and $\arg P(z)$ are established for an algebraic polynomial $P(z)$ at points on the circle $|z|=1$. These estimates depend, in particular, on the constant term and the leading coefficient of the polynomial $P(z)$ and improve the classical Bernstein and Turan inequalities. The method of proof is based on the techniques of generalized reduced moduli. 
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V. N. Dubinin. Distortion theorems for polynomials on a circle. Sbornik. Mathematics, Tome 191 (2000) no. 12, pp. 1797-1807. http://geodesic.mathdoc.fr/item/SM_2000_191_12_a2/

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