Complex and p-Adic Meromorphic Functions f′P′( f ),g′P′(g) Sharing a Small Function  

作　　者：Alain Escassut Kamal Boussaf Jacqueline Ojeda 

机构地区：[1]Laboratoire de Mathematiques, UMR 6620, Universit'e Blaise Pascal,Les C'ezeaux,Aubiere 63171, France [2]Departamento de Matematica, Facultad de Ciencias Fsicasy Matematicas,Universidad de Concepcion,Concepcion, Chile

出　　处：《Analysis in Theory and Applications》2014年第1期51-81,共31页分析理论与应用（英文刊）

基　　金：Partially funded by the research project CONICYT (Inserción de nuevos investigadores en la academia, NO. 79090014) from the Chilean Government

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 prob-lems, 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 pa-per 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.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 prob-lems, 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 pa-per 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.

关 键 词：MEROMORPHIC NEVANLINNA sharing value unicity distribution of values. 

分 类 号：O174.52[理学—数学] O187[理学—基础数学]