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On a question of Gross concerning uniqueness of entire functions

Published online by Cambridge University Press:  17 April 2009

Hong-Xun Yi
Hong-Xun Yi
Affiliation:
Department of MathematicsShandong UniversityJinan, Shandong 250100People's Republic of China e-mail: [email protected]
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Abstract

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In this paper, we prove that there exist two finite sets S1 (with 1 element) and S2 (with 3 elements) such that any two entire functions f and g satisfying Ef(Sj) = Eg(Sj) for j = 1, 2 must be identical. This answers a question posed by Gross. Examples are provided to show that this result is sharp.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 2 , April 1998 , pp. 343 - 349
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Gross, F., ‘Factorization of meromorphic functions and some open problems’, in Complex Analysis (Proc. Conf. Univ. Kentucky, Lexington, KY, 1976), Lecture Notes in Math. 599 (Springer-Verlag, Berlin, Heidelberg, New York, 1977), pp. 51–69.Google Scholar
[2]Gundersen, G.G., ‘Meromorphic functions that share three or four values’, J. London Math. Soc. 20 (1979), 457–466.CrossRefGoogle Scholar
[3]Hayman, W.K., Meromorphic functions (Clarendon Press, Oxford, 1964).Google Scholar
[4]Li, P., Uniqueness and value sharing of meromorphic functions (Thesis, The Hong Kong University of Science and Technology, 1996).Google Scholar
[5]Yi, Hong-Xun, ‘On a result of Gross and Yang’, Tôhoku Math. J. 42 (1990), 419–428.CrossRefGoogle Scholar
[6]Yi, Hong-Xun, ‘Uniqueness of meromorphic functions and question of Gross’, Science in China (Series A) 37 (1994), 802–813.Google Scholar
[7]Yi, Hong-Xun, ‘Meromorphic functions that share one or two values’, Complex Variables Theory Appl. 28 (1995), 1–11.Google Scholar
[8]Yi, Hong-Xun, ‘The unique range sets for entire or meromorphic functions’, Complex Variables Theory Appl. 28 (1995), 13–21.Google Scholar
[9]Yi, Hong-Xun and Yang, C.C., ‘A uniqueness theorem for meromorphic functions whose n-th derivatives share the same 1-points’, J. D'Analyse Math. 62 (1994), 261–270.CrossRefGoogle Scholar
[10]Yi, Hong-Xun and Yang, C.C., Uniqueness theory of meromorphic functions (Science Press, Beijing, 1995).Google Scholar