Abstract
UDC 517.9 Two meromorphic functions f and g are said to share the set S ⊂ ℂ ∪ { ∞ } with weight l ∈ ℕ ∪ { 0 } ∪ { ∞ } , if E f ( S , l ) = E g ( S , l ) , where where t = p if p ≤ l and t = p + 1 if p > l . In this paper, we improve and supplement the result of L. W. Liao and C. C. Yang [Indian J. Pure and Appl. Math., <strong>31</strong>, No~4, 431–440 (2000)] by showing that there exist a finite set S with 13 elements such that E f ( S ,1 ) = E g ( S ,1 ) implies f ≡ g .
Highlights
Introduction and Definitions By C andN, we mean the set of complex numbers and set of natural numbers respectively
By C and N, we mean the set of complex numbers and set of natural numbers respectively
We mean an analytic function defined on C except possibly at isolated singularities, each of which is a pole
Summary
Let f and g be two non-constant meromorphic functions satisfying Ef (S, 1) = Eg(S, 1). Suppose that n(≥ 1) be a positive integer. Further suppose that S = {z : P (z) = 0} where the polynomial P (z) of degree n defined by (1.1). Let f and g be two non-constant entire functions satisfying Ef (S, 1) = Eg(S, 1).
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