The value distribution of differential polynomials is studied. The results in this paper improve and generalize some previous theorems given by Yang Chungchun （On deficiencies of differential polynomials, Math. Z., ...The value distribution of differential polynomials is studied. The results in this paper improve and generalize some previous theorems given by Yang Chungchun （On deficiencies of differential polynomials, Math. Z., 116（1970）, 197- 204）, H. S. Gopalakrishna and S. S. Bhoosnurmath （On distribution of values of differential polynomials, Indian 3. Pure Appl. Math., 17（1986）, 367-372）, I. Lahiri （A note on distribution of nonhomogeneous differential polynomials, Hokkaido Math. J., 31（2002）, 453-458） and Yi Hongxun （On zeros of differential polynomials, Adv. in Math., 18（1989）, 335-351） et al. Examples show that the results in this paper are sharu.展开更多
In this paper,we use the theory of value distribution and study the uniqueness of meromorphic functions.We will prove the following result:Let f(z)and g(z)be two transcendental meromorphic functions,p(z)a polynomial o...In this paper,we use the theory of value distribution and study the uniqueness of meromorphic functions.We will prove the following result:Let f(z)and g(z)be two transcendental meromorphic functions,p(z)a polynomial of degree k,n≥max{11,k+1}a positive integer.If fn(z)f(z)and gn(z)g(z)share p(z)CM,then either f(z)=c1ec p(z)dz, g(z)=c2e ?c p(z)dz ,where c1,c2 and c are three constants satisfying(c1c2) n+1 c2=-1 or f(z)≡tg(z)for a constant t such that tn+1=1.展开更多
文摘The value distribution of differential polynomials is studied. The results in this paper improve and generalize some previous theorems given by Yang Chungchun （On deficiencies of differential polynomials, Math. Z., 116（1970）, 197- 204）, H. S. Gopalakrishna and S. S. Bhoosnurmath （On distribution of values of differential polynomials, Indian 3. Pure Appl. Math., 17（1986）, 367-372）, I. Lahiri （A note on distribution of nonhomogeneous differential polynomials, Hokkaido Math. J., 31（2002）, 453-458） and Yi Hongxun （On zeros of differential polynomials, Adv. in Math., 18（1989）, 335-351） et al. Examples show that the results in this paper are sharu.
基金Supported by the Natural Science Foundation of Jiangsu Education Department（07KJD110086）
文摘In this paper,we use the theory of value distribution and study the uniqueness of meromorphic functions.We will prove the following result:Let f(z)and g(z)be two transcendental meromorphic functions,p(z)a polynomial of degree k,n≥max{11,k+1}a positive integer.If fn(z)f(z)and gn(z)g(z)share p(z)CM,then either f(z)=c1ec p(z)dz, g(z)=c2e ?c p(z)dz ,where c1,c2 and c are three constants satisfying(c1c2) n+1 c2=-1 or f(z)≡tg(z)for a constant t such that tn+1=1.
