Geodesic
Critical values and moduli of derivative of a~complex polynomial at its zeros
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 32, Tome 449 (2016), pp. 60-68

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Under some restrictions on critical values of an algebraic polynomial with complex coefficients, a sharp inequality for the product of certain powers of moduli of its derivatives at its zeros is established. The equality is attained for the suitable Chebyshev polynomial of the first kind. 
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     author = {V. N. Dubinin},
     title = {Critical values and moduli of derivative of a~complex polynomial at its zeros},
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V. N. Dubinin. Critical values and moduli of derivative of a~complex polynomial at its zeros. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 32, Tome 449 (2016), pp. 60-68. http://geodesic.mathdoc.fr/item/ZNSL_2016_449_a3/