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Uniqueness of meromorphic functions and weighted sharing. (English) Zbl 1207.30048

The paper under review deals with the uniqueness problem of meromorphic functions. By the help of the notion of weighted sharing of values, the authors improve a result on uniqueness of meromorphic functions of P. Li [Kodai Math. J. 21, No. 2, 138–152 (1998; Zbl 0930.30027)]:
Let \(f(z)\) and \(g(z)\) be two non-constant meromorphic functions sharing \((0,1)\), \((1,\infty)\), \((\infty,\infty)\). If there exists a complex number \(a\) (\(\neq 0,1,\infty \)) such that \[ T(r,f)\leq c\overline{N}(r,a;f|\geq2)+S(r,f), \] then \(f(z)\) and \(g(z)\) share \((0,\infty)\), \((1,\infty)\), \((\infty,\infty)\), where \(c\) \((>0)\) is a constant and \(\overline{N}(r,a;f|\geq s)\) denotes the counting function of those \(a\)-points of \(f(z)\) whose multiplicities are greater than or equal to \(s\), where each \(a\)-point is counted only once.

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory

Citations:

Zbl 0930.30027
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