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Title: Some further results on the unique range sets of meromorphic functions
Authors: Li, Ping
Yang, Chung-Chun
Keywords: Meromorphic function
Entire function
Unique range set
Uniqueness polynomial
Issue Date: 1995
Citation: Kōdai mathematical journal, v. 18, 1995, p. 437-450
Abstract: By improving a generalization of Borel's theorem, the authors have been able to show that there exists a finite set S with 15 elements such that for any two nonconstant meromorphic functions f and g the condition Ef(S)=Eg(S) implies f≡g. As a special case this also answers an open question posed by Gross [1] about entire functions, and has improved some results obtained recently by Yi [10]. In the last section, the uniqueness polynomials of meromorphic functions which is related to the unique range sets has been studied. A necessary and sufficient condition for a polynomial of degree 4 to be a uniqueness polynomial is obtained.
Rights: © Department of Mathematics, Tokyo Institute of Technology. Reproduced with permission.
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