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A counterexample to the Arakelyan conjecture
Author(s):
A.
Erëmenko
Journal:
Bull. Amer. Math. Soc.
27
(1992),
159-164.
MSC (2000):
Primary 30D35;
Secondary 30D15, 31A05
MathSciNet review:
1145577
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Additional information
Abstract:
A "self-similar" example is constructed that shows that a conjecture of N. U. Arakelyan on the order of decrease of deficiencies of an entire function of finite order is not true.
References:
-
- [1]
- J. Anderson and A. Baernstein, The size of the set on which a meromorphic function is large, Proc. London Math. Soc. (3) 36 (1983), 518-539. MR 0481006 (58:1153)
- [2]
- N. U. Arakelyan, Entire functions of finite order with an infinite set of deficient values, Doklady Akad. Nauk. SSSR 170 (1966), 999-1002; English transl. Soviet Math. Dokl. 7 (1966), 1303-1306. MR 0206286 (34:6105)
- [3]
- A. Eremenko, On the set of deficient values of entire function of finite order, Ukrainian Math. J. 39 (1987), 225-228. (English translation) MR 899492 (88j:30066)
- [4]
- A. Eremenko, Inverse problem of value distribution theory for meromorphic functions of finite order, Siberian Math. J. 27 (1987), 377-390. (English translation)
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- [6]
- A. Eremenko and M. Sodin, Distribution of values of meromorphic functions and meromorphic curves from the point of view of potential theory, Algebra & Analysis 3 (1991), 131-164. (English translation) MR 1120844 (93a:32003)
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- W. H. J. Fuchs, Théorie de l'approximation des fonctions d'une variable complexe, Université de Montréal, 1968. MR 0261010 (41:5630)
- [8]
- A. A. Goldberg and I. V. Ostrovskii, Distribution of values of meromorphic functions, Moscow, 1970. (Russian) MR 0280720 (43:6439)
- [9]
- W. Hayman, Meromorphic Functions, Oxford University Press, 1964. MR 0164038 (29:1337)
- [10]
- J. Lewis and Jang-Mei Wu, On Conjectures of Arakelyan and Littlewood, J. Analyse Math. 50 (1988), 259-283. MR 942832 (89i:30038)
- [11]
- A. Weitsman, A theorem on Nevanlinna deficiencies, Acta Math. 128 (1972), 41-52. MR 0387597 (52:8437)
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Additional Information:
DOI:
10.1090/S0273-0979-1992-00299-9
PII:
S 0273-0979(1992)00299-9
Copyright of article:
Copyright
1992,
American Mathematical Society
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