Abstract
In this paper, we prove several results concerning meromorphic functions f and g of hyperorder less than one such that f (j) and g (j) have the same zeros and poles for j = 0, 1, 2. We provide some examples to show that our results are sharp.
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References
Hayman, W. K.: Meromorphic Functions, Clarendon Press, Oxford, 1964
Yang, L.: Value Distribution Theory, Springer-Verlag, Berlin, 1993
Yi, H. X., Yang, C. C.: Uniqueness Theory of Meromorphic Functions, Science Press, Beijing, Chinese, 1995
Barth, K. F., Brannan, D. A., Hayman, W. K.: Research problems in complex analysis. Bull. London Math. Soc., 16, 490–517 (1984)
Gundersen, G.: When two entire functions and also their first derivatives have the same zeros. Indiana Univ. Math. J., 30, 293–303 (1981)
Yang, C. C.: On two entire functions which together with their first derivatives have the same zeros. J. Math. Anal. Appl., 56, 1–6 (1976)
Köhler, L.: Meromorphic functions sharing zeros and poles and also some of their derivatives sharing zeros. Complex Variables Theory Appl., 11, 39–48 (1989)
Köhler, L.: Meromorphe Funktionen mit gleichen Nullstellen und Polstellen und jeweils gleichen Nullstellen einiger Ableitungen, Doktordissertation, Hannover, 1987
Tohge, K.: On a problem of Hinkkanen about Hadamard products. Kodai Math. J., 13, 101–120 (1990)
Langley, J. K.: Two results related to a question of Hinkkanen. Kodai Math. J., 19, 56–61 (1996)
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This work is supported by the NNSF of China (No. 10371065) and the NSF of Shandong Province, China (No. Z2002A01)
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Yang, L.Z., Yi, H.X. Some Results Related to a Question of Hinkkanen. Acta Math Sinica 23, 1405–1412 (2007). https://doi.org/10.1007/s10114-005-0848-2
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DOI: https://doi.org/10.1007/s10114-005-0848-2