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On Osgood-Yang’s conjecture and Mues conjecture

  • Hong-Xun Yi (a1) and Yu-Hua Li (a2)

Abstract

In this paper, we deal with the relation between the characteristic functions of meromorphic functions that share three values CM. As applications of our main results, we shall affirmatively settle two conjectures proposed by Mues and Osgood-Yang.

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References

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[1] Hayman, W. K., Meromorphic Functions, Clarendon Press, Oxford, 1964.
[2] Gundersen, G. G., Meromorphic functions that share three or four values, J. London Math. Soc., 20 (1979), 457466.
[3] Osgood, C. F. and Yang, C. C., On the quotient of two integral functions, J. Math Anal Appl., 54 (1976), 408418.
[4] Brosch, G., Eindeutigkeitssätze für meromorphe Funktionen, Thesis, Technical University of Aachen, 1989.
[5] Bergweiler, W., On meromorphic functions that share three and on the exceptional set in Wiman-Valiron theory, Kodai Math. J., 14 (1990), 19.
[6] Mues, E., Shared value problems for meromorphic functions, Value Distribution Theory and Complex Differential Equations, Univ. of Joensuu, Publications in Sci. No. 35, Joensuu, 1995, 1743.
[7] Li, P. and Yang, C. C., On the characteristics of meromorphic functions that share three values CM, J. Math. Anal. Appl., 220 (1998), 132145.
[8] Yi, H. X. and Yang, C. C., Uniqueness Theory of Meromorphic Functions, Pure and Applied Math. Monographs No. 32, Science Press, Beijing, 1995.
[9] Mokhon’ko, A. Z., On Nevanlinna characteristics of some meromorphic functions, Theory of Functions, Functional Analysis and Their Applications, 14 (1971), 8387.
[10] Zhang, Q. C., Meromorphic functions sharing three values, Indian J. Pure Appl. Math., 30 (1999), 667682.
[11] Yi, H. X., On a result of Gross and Yang, Tôhoku Math. J., 42 (1990), 419428.
[12] Yi, H. X., Unicity theorems for meromorphic functions that share three values, Kodai Math. J., 18 (1995), 300314.
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On Osgood-Yang’s conjecture and Mues conjecture

  • Hong-Xun Yi (a1) and Yu-Hua Li (a2)

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