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Entire and Meromorphic Functions with Asymptotically Prescribed Characteristic

Published online by Cambridge University Press:  20 November 2018

Albert Edrei  and
Wolfgang H. J. Fuchs
Albert Edrei
Affiliation:
Cornell University
Wolfgang H. J. Fuchs
Affiliation:
Cornell University
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If f(z) is a non-constant, entire function, then Hadamard's three-circles theorem asserts that

is a convex, increasing function of log r. Hence, by well-known properties of logarithmically convex functions,

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 383 - 395
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Alpar, L. and P. Turán, Sur la distribution des valeurs d'une fonction entière, Magyar Tud. Akad. Mat. Kukatö Int. Közl., 6 (1961), 157–161.Google Scholar
2. Bloch, A., Les fonctions holomorphes et méromorphes dans le cercle-unité, Mém. Sci. math., XX (Paris, 1926).Google Scholar
3. Edrei, A. and W. H. J. Fuchs, Bounds for the number of deficient values of certain classes of meromorphic functions, Proc. London Math. Soc, 12 (1962), 315–344.Google Scholar
4. Nevanlinna, R., Le théorème de Picard-Borel et la théorie des fonctions méromorphes (Paris, 1930).Google Scholar
5. Nevanlinna, R., Eindeutige analytische Funktionen, 2nd éd. (Berlin, 1953).Google Scholar
6. Valiron, G., Sur les fonctions entières d'ordre fini et d'ordre nul, et en particulier les fonctions à correspondance régulière, Ann. Fac. Sci. Toulouse, 5(3) (1913), 117–208.Google Scholar