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Some Results Related to a Question of Hinkkanen

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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

  1. Hayman, W. K.: Meromorphic Functions, Clarendon Press, Oxford, 1964

  2. Yang, L.: Value Distribution Theory, Springer-Verlag, Berlin, 1993

  3. Yi, H. X., Yang, C. C.: Uniqueness Theory of Meromorphic Functions, Science Press, Beijing, Chinese, 1995

  4. Barth, K. F., Brannan, D. A., Hayman, W. K.: Research problems in complex analysis. Bull. London Math. Soc., 16, 490–517 (1984)

    Article  MATH  Google Scholar 

  5. Gundersen, G.: When two entire functions and also their first derivatives have the same zeros. Indiana Univ. Math. J., 30, 293–303 (1981)

    Article  MATH  Google Scholar 

  6. 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)

    Article  MATH  Google Scholar 

  7. Köhler, L.: Meromorphic functions sharing zeros and poles and also some of their derivatives sharing zeros. Complex Variables Theory Appl., 11, 39–48 (1989)

    MATH  Google Scholar 

  8. Köhler, L.: Meromorphe Funktionen mit gleichen Nullstellen und Polstellen und jeweils gleichen Nullstellen einiger Ableitungen, Doktordissertation, Hannover, 1987

  9. Tohge, K.: On a problem of Hinkkanen about Hadamard products. Kodai Math. J., 13, 101–120 (1990)

    Article  MATH  Google Scholar 

  10. Langley, J. K.: Two results related to a question of Hinkkanen. Kodai Math. J., 19, 56–61 (1996)

    Article  Google Scholar 

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Correspondence to Lian Zhong Yang or Hong Xun Yi.

Additional information

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

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