Lahiri, Indrajit; Pal, Rupa Uniqueness of meromorphic functions and weighted sharing. (English) Zbl 1207.30048 Aust. J. Math. Anal. Appl. 7, No. 1, Article No. 18, 7 p. (2010). 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. Reviewer: Yinying Kong (Vannes) MSC: 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory Keywords:uniqueness; meromorphic functions; weighted sharing Citations:Zbl 0930.30027 PDFBibTeX XMLCite \textit{I. Lahiri} and \textit{R. Pal}, Aust. J. Math. Anal. Appl. 7, No. 1, Article No. 18, 7 p. (2010; Zbl 1207.30048) Full Text: Link