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On the unique range set of meromorphic functions

Author(s): Ping Li; Chung-Chun Yang
Journal: Proc. Amer. Math. Soc. 124 (1996), 177-185.
MSC (1991): Primary 30D35
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Abstract: This paper studies the unique range set of meromorphic functions and shows that there exists a finite set $S$ such that for any two nonconstant meromorphic functions $f$ and $g$ the condition $E_f(S)=E_g(S)$ implies $f\equiv g$ . As a special case this also answers an open question posed by Gross (1977) about entire functions and improves some results obtained recently by Yi.

References:

1: F. Gross, Complex analysis, Lecture Notes in Math., vol. 599, Springer, Berlin and New York, 1977 pp. 51--69
2: F. Gross and C. C. Yang, On preimage and range sets of meromorphic functions, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982), 17--20 MR 83d:30027
3: F. Gross, Factorizations of meromorphic functions, U.S. Government Printing Office Publication, Washington D.C., 1972.
4: W. K. Hayman, Meromorphic functions, Clarendon Press, Oxford, 1964. MR 29:6019
5: C. C. Yang, On deficiencies of differential polynomials, II Math. Z. 125 (1972) 107--112. MR 45:3710
6: Hongxun Yi, On a problem of Gross, Sci. China Ser. A 11 (24) (1994), 1137--1144.
7: ------, Meromorphic functions that share three values, Chinese Ann. Math. Ser. A 9 (1988) 434--439. MR 90f:30039


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