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Coefficients of odd univalent functions

Author: Ke Hu
Journal: Proc. Amer. Math. Soc. 96 (1986), 183-186
MSC: Primary 30C50; Secondary 30C45
MathSciNet review: 813835
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Abstract: Let

$\displaystyle {S_2} = \left\{ {{f_2}(z) = z + \sum\limits_{n = 1}^\infty {{b_n}{z^{2n + 1}}} \in S} \right\}.$

In this note we prove $ \left\vert {{b_n}} \right\vert < 1.1305$. This is an improvement of V. I. Milin's result [1].

References [Enhancements On Off] (What's this?)

  • [1] V. I. Milin, Estimate of the coefficients of odd univalent functions, Metric Questions of the Theory of Functions (G. D. Suvorov, ed.), "Naukova Dumka", Kiev, 1980, pp. 78-86. (Russian) MR 598843 (82i:30025)
  • [2] I. M. Milin, Univalent functions and orthonormal systems, "Nauka", Moscow, 1971; English transl. in Transl. Math. Monographs, vol. 49, Amer. Math. Soc., Providence, R. I., 1977. MR 0369684 (51:5916)
  • [3] V. I. Levin, Some remarks on the coefficients of schlicht functions, Proc. London Math. Soc. 39 (1935), 467-480.
  • [4] J. E. Littlewood and R. E. A. C. Paley, A proof that an odd schlicht function has bounded coefficients, J. London Math. Soc. 7 (1932), 167-169.
  • [5] Kung Sun, Contributions to the theory of schlicht functions. II: The coefficient problem, Sci. Sinica 4 (1955), 359-373.
  • [6] L. de Branges, A proof of the Bieberbach conjecture, Steklov Mat. Inst., LOMI, preprint E-5-84, Leningrad, 1984, pp. 1-21.

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