Geodesic
An Extremal Problem for the Derivative of a Rational Function
Matematičeskie zametki, Tome 100 (2016) no. 5, pp. 732-738.

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Erdős' well-known problem on the maximum absolute value of the derivative of a polynomial on a connected lemniscate is extended to the case of a rational function. Moreover, under the assumption that certain lemniscates are connected, a sharp upper bound for the absolute value of the derivative of a rational function at any point in the plane different from the poles is found. The role of the extremal function is played by an appropriate Zolotarev fraction.
Keywords: rational function, lemniscate, Riemann surface, symmetrization.
Mots-clés : Zolotarev fraction 
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V. N. Dubinin. An Extremal Problem for the Derivative of a Rational Function. Matematičeskie zametki, Tome 100 (2016) no. 5, pp. 732-738. http://geodesic.mathdoc.fr/item/MZM_2016_100_5_a7/

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