Li, Ping Meromorphic functions sharing three values or sets CM. (English) Zbl 0930.30027 Kodai Math. J. 21, No. 2, 138-152 (1998). In addition to the usual terminology of Nevanlinna theory, let \(\overline{N}_{k)}(r,1/(f-a))\) and \(\overline{N}_{(k}(r,1/(f-a))\) be the reduced counting functions of the \(a\)-points of a meromorphic function \(f\) which have multiplicity at most \(k\) or at least \(k\), respectively. It is shown in Theorem 1 that if \(f\) and \(g\) are meromorphic functions which share 0,1,\(\infty\) counting multiplicity and which are not Möbius transformations of each other, and if there exists \(a\not=0,1,\infty\) such that \({T(r,f)\leq c\overline{N}_{(2}(r,{{1}\over{f-a}})+S(r,f)}\) for some \(c>0\), then \(f\) and \(g\) have the form \({f={{{e^{t\gamma}-1}\over{\lambda e^{-s\gamma}-1}}}, g={{{e^{-t\gamma}-1}\over{{{1}\over{\lambda}} e^{s\gamma}-1}}}}\) where \(\gamma\) is a non-constant entire function, \(\lambda\) a non-zero constant and \(s\) and \(t\) are mutually prime integers, \(t>0\). Moreover, \(\theta:=-t/s\not=1,a\) and \({{{(1-a)^{s+t}}\over{a^t}}=\lambda^t{{(1-\theta)^{s+t}}\over{\theta^t}}}\). Theorem 2 gives a result of this type if \({\overline{N}_{1)}(r,{{1}\over{f-a}})=S(r,f)}\). Here \(f\) and \(g\) have one of nine possible forms, which are listed explicitly. Theorem 3 gives a result for functions sharing sets. Reviewer: W.Bergweiler (Kiel) Cited in 1 ReviewCited in 3 Documents MSC: 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory Keywords:shared values; meromorphic; Nevanlinna theory PDFBibTeX XMLCite \textit{P. Li}, Kodai Math. J. 21, No. 2, 138--152 (1998; Zbl 0930.30027) Full Text: DOI References: [1] W. BERGWEILER, On meromorphic functions that share three values and on the exceptional set in Wiman-Valiron theory, Kodai Math. J., 13 (1990), pp. 1-9. · Zbl 0708.30030 [2] G. BROSCH, Eindeutigkeitssatze fur meromorphe Funktionen, Thesis, Technical University o Aachen, 1989. · Zbl 0694.30027 [3] F. GROSS AND C. C. YANG, Meromorphic functions coveng certain finite sets at the sam points, Illinois J. Math., 26 (1982), pp. 432-441. · Zbl 0503.30029 [4] E. MUES, Shared value problems for meromorphic functions, Value Distribution Theory An Complex Differential Equations, Joensuu, 1994, Univ. Joensuu, 1995, pp. 17-43. · Zbl 0951.30027 [5] R. NEVANLINNA, Einige Eindentigkeitssatze in der Theoe der Meromorphen Funktionen, Acta Math., 48 (1926), pp. 367-391 · JFM 52.0323.03 [6] P. Li AND C. C. YANG, On the characteristics of meromorphic functions that share three value CM, J. Math. Anal. Appl, 220 (1998), pp. 132-145. · Zbl 0909.30021 [7] U. STRAHMANN, Eindeutigkeitssatze fur meromorphe Funktionen, die nebst ihren Ableitunge Werte teilen, Thesis, University of Hannover, 1993. [8] H. UEDA, Umcity theorems for meromorphic or entire functions II, Kodai Math. J., 6 (1983), pp. 26-36 · Zbl 0518.30029 [9] S. -Z. YE, Uniqueness of meromorphic functions that share three values, Kodai Math. J., 1 (1992), pp. 236-243. · Zbl 0767.30026 [10] H. X. Yi, On the meromorphic function that cover three finite sets at same points, J. Shandong Univ. Nat. Sci. Ed., 22 (1987), pp. 41-53 (in Chinese) · Zbl 0632.30035 [11] H. X. Yi, Meromorphic functions that share two or three values, Kodai Math. J., 13 (1990), pp. 363-372 · Zbl 0712.30029 [12] H. X. Yi AND C. C. YANG, Uniqueness Theory of Meromorphic Functions, Science Press, China, 1995 (in Chinese) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.