There have been lots of papers on the uniqueness theory of entire functions concerning shared-sets in the whole complex plane. However, it seems that the uniqueness theory in an angular domain is not widely investigat...There have been lots of papers on the uniqueness theory of entire functions concerning shared-sets in the whole complex plane. However, it seems that the uniqueness theory in an angular domain is not widely investigated. In this paper, we study the uniqueness of entire functions concerning shared-sets in an angular domain instead of the whole complex plane, and we supply examples to show that Theorem 1 is sharp.展开更多
In this paper,uniqueness of entire function related to shared set is studied.Let f be a non-constant entire function and k be a positive integer,d be a finite complex number.There exists a set S with 3 elements such t...In this paper,uniqueness of entire function related to shared set is studied.Let f be a non-constant entire function and k be a positive integer,d be a finite complex number.There exists a set S with 3 elements such that if f and its derivative f（k）satisfy E（S,f）= E（S,f（k））,and the zeros of f（z）-d are of multiplicity ≥ k ＋ 1,then f = f（k）.展开更多
In this paper, we prove the following theorem: Suppose that k , n be two positive integers, and a , b , w be three finite complex numbers with a n≠b n , w n=1 . If a meromorphic function f...In this paper, we prove the following theorem: Suppose that k , n be two positive integers, and a , b , w be three finite complex numbers with a n≠b n , w n=1 . If a meromorphic function f(z) and its k-th derivative f (k) (z) share two finite set S 1={aw i | i=1,2,…, n} , S 2={bw i | i=1,2,…,n} , then f(z)=tf (k) (z) , where t n=1.展开更多
In this paper, we deal with the problem of uniqueness of meromorphic functions. It is shown that there exist two finite sets Sj (j=1, 2) such that any two nonconstant meromorphic functions f and g satisfying Ef(Sj)=Eg...In this paper, we deal with the problem of uniqueness of meromorphic functions. It is shown that there exist two finite sets Sj (j=1, 2) such that any two nonconstant meromorphic functions f and g satisfying Ef(Sj)=Eg(Sj) for j = 1,2 must be identical, which answers a question posed by Gross.展开更多
基金the National Natural Science Foundation of China (10671109)the Research Foundation of Doctor Points of China (20060422049)+1 种基金the JSPS Post Doctoral Fellowship Programthe Fujian Province Natural Science Foundation (2008J0190)
文摘There have been lots of papers on the uniqueness theory of entire functions concerning shared-sets in the whole complex plane. However, it seems that the uniqueness theory in an angular domain is not widely investigated. In this paper, we study the uniqueness of entire functions concerning shared-sets in an angular domain instead of the whole complex plane, and we supply examples to show that Theorem 1 is sharp.
基金Supported by the Natural Science Foundation of Anhui Province (Grant No. KJ2010B124)
文摘In this paper,uniqueness of entire function related to shared set is studied.Let f be a non-constant entire function and k be a positive integer,d be a finite complex number.There exists a set S with 3 elements such that if f and its derivative f（k）satisfy E（S,f）= E（S,f（k））,and the zeros of f（z）-d are of multiplicity ≥ k ＋ 1,then f = f（k）.
文摘In this paper, we prove the following theorem: Suppose that k , n be two positive integers, and a , b , w be three finite complex numbers with a n≠b n , w n=1 . If a meromorphic function f(z) and its k-th derivative f (k) (z) share two finite set S 1={aw i | i=1,2,…, n} , S 2={bw i | i=1,2,…,n} , then f(z)=tf (k) (z) , where t n=1.
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper, we deal with the problem of uniqueness of meromorphic functions. It is shown that there exist two finite sets Sj (j=1, 2) such that any two nonconstant meromorphic functions f and g satisfying Ef(Sj)=Eg(Sj) for j = 1,2 must be identical, which answers a question posed by Gross.
