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Abstract. Introducing the idea of weighted sharing of values we prove some uniqueness theorems for meromorphic functions which improve some existing results. §1. Introduction and DefinitionsLet f and g be two nonconstant meromorphic functions defined in the open complex plane C. If for some a ∈ C ∪ {∞} the a-points of f and g coincide in locations and multiplicities, we say that f and g share the value a CM (counting multiplicities). On the other hand, if the a-points of f and g coincide in locations only, we say that f and g share the value a IM (ignoring multiplicities).Though we do not explain the standard notations of the value distribution theory because those are available in [2], we explain some notations which will be needed in the sequel. Definition 1. If s is a nonnegative integer, we denote by N (r, a; f |= s) the counting function of those a-points of f whose multiplicity is s, where each a-point is counted according to its multiplicity.Definition 2. If s is a positive integer, we denote by N (r, a; f |≥ s) the counting function of those a-points of f whose multiplicities are greater than or equal to s, where each a-point is counted only once.Definition 3. If s is a nonnegative integer, we denote by N s (r, a; f ) the counting function of a-points of f where an a-point with multiplicity m is counted m times if m ≤ s and s times if m > s. We put N ∞ (r, a; f ) = N (r, a; f ).

Abstract. We prove a result on the value distribution of differential polynomials which improves some earlier results.

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We prove a uniqueness theorem for meromorphic functions involving linear differential polynomials generated by them. As consequences of the main result we improve some previous results.