ある意味で1つの集合と2つの値を共有する有理型函数,II
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概要
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In this paper we give a unicity theorem for nonconstant meromorphic functions in the whole complex plane C that share one set Sn and two values in some sense. Our result is the following: Let S_n = {ω : ω^n(ω + a) - b = 0} with an integer n ≧ 4 and two nonzero constants a,b such that the algebraic equation ω^n(ω + a) - b = 0 has no multiple roots. Assume that f and g are distinct nonconstant meromorphic Junctions in the whole complex plane C sharing one set S_n with finite weight l ≧ 1 and two values 0,∞ IM. If two positive integers l and n satisfy the relation (*) ln^3 - (2l + 3)n^2 - 6(l + 1)n + l - 1 > 0, then f and g are the following forms: [numerical formula] where a is a nonconstant entire function. (Remark) (1) If l = 1, then n ≧ 7 satisfies the above(*). (2) If l = 2, then n ≧ 6 satisfies the above(*). (3) If l = 3, then n ≧ 5 satisfies the above(*). (4) If l = 9, then n ≧ 4 satisfies the above(*).
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