The dispersion of the coefficients of univalent functions

Author:
D. H. Hamilton

Journal:
Trans. Amer. Math. Soc. **276** (1983), 323-333

MSC:
Primary 30C50

MathSciNet review:
684512

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Abstract: The Hayman function for the asymptotic distribution of the coefficients of univalent functions has a continuous derivative which is closely related to the asymptotic behavior of coefficient differences.

**[1]**Enrico Bombieri,*On functions which are regular and univalent in a half-plane*, Proc. London Math. Soc. (3)**14a**(1965), 47–50. MR**0185108****[2]**Enrico Bombieri,*On the local maximum property of the Koebe function*, Invent. Math.**4**(1967), 26–67. MR**0218549****[3]**C. H. FitzGerald,*Large late coefficients of univalent functions*(to appear).**[4]**W. K. Hayman,*On successive coefficients of univalent functions*, J. London Math. Soc.**38**(1963), 228–243. MR**0148885****[5]**-,*On a conjecture of Littlewood*, Proc. Amer. Math. Soc. (to appear).**[6]**David H. Hamilton,*The equivalence of two weak Bieberbach conjectures*, Math. Z.**181**(1982), no. 2, 191–195. MR**674271**, 10.1007/BF01215018**[7]**W. K. Hayman,*Bounds for the large coefficients of univalent functions*, Ann. Acad. Sci. Fenn. Ser. A.I, no.**250/13**(1958), 13. MR**0096810****[8]**W. K. Hayman,*On successive coefficients of univalent functions*, J. London Math. Soc.**38**(1963), 228–243. MR**0148885****[9]**D. Horowitz (to appear).**[10]**K. W. Lucas,*On successive coefficients of areally mean 𝑝-valent functions*, J. London Math. Soc.**44**(1969), 631–642. MR**0243055****[11]**Zeev Nehari,*On the coefficients of univalent functions*, Proc. Amer. Math. Soc.**8**(1957), 291–293. MR**0083569**, 10.1090/S0002-9939-1957-0083569-3

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DOI:
https://doi.org/10.1090/S0002-9947-1983-0684512-6

Article copyright:
© Copyright 1983
American Mathematical Society