Geodesic
An upper bound for the least critical values of finite Blaschke products
Sbornik. Mathematics, Tome 213 (2022) no. 6, pp. 744-751

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For the finite Blaschke products $B$ of degree $n\geqslant2$ such that $B(0)=0$ and $ B'(0)\ne0$, the supremum of the minimum moduli of their critical values is found which depends only on $n$ and $|B'(0)|$. Bibliography: 12 titles.
Keywords: rational functions, Blaschke products, critical values, Riemann surfaces, dissymmetrization. 
V. N. Dubinin. An upper bound for the least critical values of finite Blaschke products. Sbornik. Mathematics, Tome 213 (2022) no. 6, pp. 744-751. http://geodesic.mathdoc.fr/item/SM_2022_213_6_a1/
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[1] J. Mashreghi and E. Fricain (eds.), Blaschke products and their applications (Toronto, ON 2011), Fields Inst. Commun., 65, Springer, New York; Fields Institute for Research in Mathematical Sciences, Toronto, ON, 2013, x+319 pp. | DOI | MR | Zbl

[2] Tuen Wai Ng and Chiu Yin Tsang, “Chebyshev-Blaschke products: solutions to certain approximation problems and differential equations”, J. Comput. Appl. Math., 277 (2015), 106–114 | DOI | MR | Zbl

[3] Tuen Wai Ng and Yongquan Zhang, “Smale's mean value conjecture for finite Blaschke products”, J. Anal., 24:2 (2016), 331–345 | DOI | MR | Zbl

[4] S. R. Garcia, J. Mashreghi and W. T. Ross, Finite Blaschke products and their connections, Springer, Cham, 2018, xix+328 pp. | DOI | MR | Zbl

[5] T. Sheil-Small, Complex polynomials, Cambridge Stud. Adv. Math., 75, Cambridge Univ. Press, Cambridge, 2002, xx+428 pp. | DOI | MR | Zbl

[6] V. N. Dubinin, “Distortion and critical values of the finite Blaschke product”, Constr. Approx., 55:2 (2022), 629–639 | DOI | MR | Zbl

[7] V. Dimitrov, A proof of the Schinzel-Zassenhaus conjecture on polynomials, arXiv: 1912.12545

[8] V. N. Dubinin, “Inequalities for critical values of polynomials”, Mat. Sb., 197:8 (2006), 63–72 ; English transl. in Sb. Math., 197:8 (2006), 1167–1176 | DOI | MR | Zbl | DOI

[9] S. Smale, “The fundamental theorem of algebra and complexity theory”, Bull. Amer. Math. Soc. (N.S.), 4:1 (1981), 1–36 | DOI | MR | Zbl

[10] V. N. Dubinin, Condenser capacities and symmetrization in geometric function theory, Dal'nauka, Vladivostok, 2009, ix+390 pp.; English transl., Springer, Basel, 2014, xii+344 pp. | DOI | MR | Zbl

[11] A. Hurwitz, Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen, Herausgegeben und ergänzt durch einen Abschnitt über geometrische Funktionentheorie von R. Courant, Grundlehren Math. Wiss., 3, 4. Aufl., Springer-Verlag, Berlin–New York, 1964, xiii+706 pp. | MR | Zbl

[12] J. A. Jenkins, Univalent functions and conformal mapping, Ergeb. Math. Grenzgeb. (N.F.), 18, Springer-Verlag, Berlin–Göttingen–Heidelberg, 1958, vi+169 pp. | DOI | MR | Zbl