Complex and p-Adic Meromorphic Functions f′P′( f ),g′P′(g) Sharing a Small Function |
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作者姓名: | Alain Escassut Kamal Boussaf Jacqueline Ojeda |
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作者单位: | [1]Laboratoire de Mathematiques, UMR 6620, Universitd Blaise Pascal, Les Cdzeaux,Aubiere 63171, France [2]Departamento de Matematica, Facultad de Ciencias Fsicasy Matematicas,Universidad de Concepcion, Concepcion, Chile |
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基金项目: | Partially funded by the research project CONICYT (Inserción de nuevos investigadores en la academia, NO. 79090014) from the Chilean Government |
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摘 要: | Let K be a complete algebraically closed p-adic field of characteristic zero.We apply results in algebraic geometry and a new Nevanlinna theorem for p-adic meromorphic functions in order to prove results of uniqueness in value sharing problems, both on K and on C. Let P be a polynomial of uniqueness for meromorphic functions in K or C or in an open disk. Let f, g be two transcendental meromorphic functions in the whole field K or in C or meromorphic functions in an open disk of K that are not quotients of bounded analytic functions. We show that if f′P′( f) and g′P′(g) share a small function α counting multiplicity, then f = g, provided that the multiplicity order of zeros of P′satisfy certain inequalities. A breakthrough in this paper consists of replacing inequalities n ≥ k+2 or n ≥ k+3 used in previous papers by Hypothesis(G). In the p-adic context, another consists of giving a lower bound for a sum of q counting functions of zeros with(q-1) times the characteristic function of the considered meromorphic function.
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关 键 词: | 超越亚纯函数 代数几何 特征函数 解析函数 计数函数 多项式 多重 零点 |
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