Uniqueness for meromorphic functions and differential polynomials
In this article, we deal with the uniqueness problems on meromorphic functions concerning differential polynomials and prove the following result: Let f and g be two transcendental meromorphic functions, a be a meromorphic function such that T(r,a)=o(T(r,f)+T(r,g)) and a \not\equiv 0,\infty. Let a be a nonzero constant. Suppose that m,n are positive integers such that n>m+10. If Yf' and Yg' share ``(0,2)", then (i) if m\geq 2, then f(z)\equiv g(z); (ii) if m=1, either f(z)\equiv g(z) or f and g satisfy the algebraic equation R(f,g)\equiv 0, where R(\varpi1,\varpi2)=(n+1)(\varpi1n+2-\varpi2n+2)-(n+2)(\varpi1n+1 -\varpi2n+1). The results in this paper improve the results of Xiong-Lin-Mori 14 and the author 12.
Uniqueness for meromorphic functions and differential polynomials
In this article, we deal with the uniqueness problems on meromorphic functions concerning differential polynomials and prove the following result: Let f and g be two transcendental meromorphic functions, a be a meromorphic function such that T(r,a)=o(T(r,f)+T(r,g)) and a \not\equiv 0,\infty. Let a be a nonzero constant. Suppose that m,n are positive integers such that n>m+10. If Yf' and Yg' share ``(0,2)", then (i) if m\geq 2, then f(z)\equiv g(z); (ii) if m=1, either f(z)\equiv g(z) or f and g satisfy the algebraic equation R(f,g)\equiv 0, where R(\varpi1,\varpi2)=(n+1)(\varpi1n+2-\varpi2n+2)-(n+2)(\varpi1n+1 -\varpi2n+1). The results in this paper improve the results of Xiong-Lin-Mori 14 and the author 12.
