On Littlewood’s conjecture for univalent functions

Hamilton, D. H.

doi:10.1090/S0002-9939-1982-0663861-6

On Littlewood’s conjecture for univalent functions
HTML articles powered by AMS MathViewer

by D. H. Hamilton PDF

Proc. Amer. Math. Soc. 86 (1982), 32-36 Request permission

Abstract:

The uniform asymptotic theory of functionals on $S$ is investigated. We prove that Littlewood’s conjecture is equivalent to the asymptotic Bieberbach conjecture of Hayman.

References

Enrico Bombieri, On functions which are regular and univalent in a half-plane, Proc. London Math. Soc. (3) 14a (1965), 47–50. MR 185108, DOI 10.1112/plms/s3-14A.1.47

Two remarks on univalent functions

Quantitative versions of the Hayman asymptotic theorem

Carl H. Fitzgerald, Quadratic inequalities and coefficient estimates for schlicht functions, Arch. Rational Mech. Anal. 46 (1972), 356–368. MR 335777, DOI 10.1007/BF00281102

Univalent functions with large late coefficients

David H. Hamilton, The equivalence of two weak Bieberbach conjectures, Math. Z. 181 (1982), no. 2, 191–195. MR 674271, DOI 10.1007/BF01215018
D. H. Hamilton, The dispersion of the coefficients of univalent functions, Trans. Amer. Math. Soc. 276 (1983), no. 1, 323–333. MR 684512, DOI 10.1090/S0002-9947-1983-0684512-6
W. K. Hayman, Multivalent functions, Cambridge Tracts in Mathematics and Mathematical Physics, No. 48, Cambridge University Press, Cambridge, 1958. MR 0108586
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

On inequalities in the theory of functions

23

Zeev Nehari, On the coefficients of univalent functions, Proc. Amer. Math. Soc. 8 (1957), 291–293. MR 83569, DOI 10.1090/S0002-9939-1957-0083569-3