Geodesic
An upper bound for the least critical values of finite Blaschke products
Sbornik. Mathematics, Tome 213 (2022) no. 6, pp. 744-751 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[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