Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T10:18:36.344Z Has data issue: false hasContentIssue false
  • English
  • Français

On the coefficients of certain automorphic functions

Published online by Cambridge University Press:  24 October 2008

W. K. Hayman ,
S. J. Patterson  and
Ch. Pommerenke
W. K. Hayman
Affiliation:
Imperial College, London, S.W. 7, England
S. J. Patterson
Affiliation:
The University, Cambridge, England
Ch. Pommerenke
Affiliation:
Technische Universität, 1 Berlin 12, Germany
Get access Rights & Permissions [Opens in a new window]

Extract

Suppose that

is regular in the unit disk D = {|z| < 1}, and assumes there values ω lying in a domain Δ. It is natural to ask what effect this restriction has on the coefficients aν. The strongest order result we can hope to prove is that

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 82 , Issue 3 , November 1977 , pp. 357 - 367
Copyright
Copyright © Cambridge Philosophical Society 1977

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Ahlfors, L. V.Zur Theorie der Überlagerungsflächen. Acta Math. 65 (1935), 157–194.CrossRefGoogle Scholar
(2)Clunie, J. G. and Hayman, W. K.Symposium on Complex Analysis, Canterbury, 1973, L. M. S. Lecture Note Series 12 (Cambridge University Press, 1974).Google Scholar
(3)Earle, C. F.Some remarks on Poincaré series. Compositio Math. 21 (1969), 167–176.Google Scholar
(4)Freud, G.Restglied eines Taubersehen Satzes: I. Acta Math. Acad. Sci. Hupgar. 2 (1951), 299–308.CrossRefGoogle Scholar
(5)Godement, R.Séries de Poincaré et Spitzenformen. Seminaire H. Cartan 10 (1957/1958).Google Scholar
(6)Hayman, W. K.Functions with values in a given domain. Proc. Amer. Math. Soc. 3 (1952), 428–432.Google Scholar
(7)Hayman, W. K. and Weitsman, A.On the coefficients and means of functions omitting values. Proc. Cambridge Philos. Soc. 77 (1975), 119–137.CrossRefGoogle Scholar
(8)Lehner, J.Lecture notes of the Cambridge L.M.S. Conference on automorphic functions, 1975.Google Scholar
(9)Littlewood, J. E.Lectures on the theory of functions (Oxford University Press, 1944).Google Scholar
(10)Magnus, W., Oberhettinger, F. and Soni, R. P.Formulas and theoremsfor the special functions of mathematical physics, 3rd ed. (Berlin, Springer, 1966).CrossRefGoogle Scholar
(11)Nevanlinna, R.Eindeutige analytische Funktionen (Berlin, Springer, 1936).CrossRefGoogle Scholar
(12)Patterson, S. J.A lattice-point problem in hyperbolic space. Mathematika 22 (1975), 81–88.CrossRefGoogle Scholar
(13)Patterson, S. J.Spectral theory and Fuchsien groups. Math. Proc. Cambridge Philos. Soc. 81 (1977), 59–75.CrossRefGoogle Scholar
(14)Pommerenke, Ch.On Bloch functions. J. London Math. Soc. (2), 2 (1970), 689–695.CrossRefGoogle Scholar
(15)Pommerenke, Ch.Estimates for normal meromorphic functions. Ann. Acad. Sci. Fenn. Ser. IA 476 (1970), 1–10.Google Scholar
(16)Roelcke, W.Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene: I. Math. Ann. 167 (1966), 292–337; II. Ibid. 168 (1967), 261–324.CrossRefGoogle Scholar
(17)Titcrmarsh, E. C.The theory of functions, 2nd ed. (Oxford University Press, 1939).Google Scholar
(18)Tauji, M.Potential theory in modern function theory (Tokyo, Maruzen, 1959).Google Scholar
(19)Widder, D. V.The Laplace transform (Princeton University Press, 1941).Google Scholar