设m(≥0)是一个正整数,h(z)(≠0)是区域D内的全纯函数,且其零点重级均≤m,P是多项式满足deg P≥3,或者degP=2且P仅有一个零点.设F是区域D内的一族亚纯函数,其零点与极点重级均≥m+1.如果对于F中的任意两个函数f,g,P(f)f′与P(g)g′分担h...设m(≥0)是一个正整数,h(z)(≠0)是区域D内的全纯函数,且其零点重级均≤m,P是多项式满足deg P≥3,或者degP=2且P仅有一个零点.设F是区域D内的一族亚纯函数,其零点与极点重级均≥m+1.如果对于F中的任意两个函数f,g,P(f)f′与P(g)g′分担h(z),则F在区域D内正规.该结果改进了Lei and Fang^([8]),Zhang^([16])等人的结果.展开更多
Let F be a family of functions meromorphic in a domain D,let P be a polynomial with either deg P≥3 or deg P=2 and P having only one distinct zero,and let b be a finite nonzero complex number.If,each pair of functions...Let F be a family of functions meromorphic in a domain D,let P be a polynomial with either deg P≥3 or deg P=2 and P having only one distinct zero,and let b be a finite nonzero complex number.If,each pair of functions f and g in F,P(f)f and P(g)g share b in D,then F is normal in D.展开更多
文摘设m(≥0)是一个正整数,h(z)(≠0)是区域D内的全纯函数,且其零点重级均≤m,P是多项式满足deg P≥3,或者degP=2且P仅有一个零点.设F是区域D内的一族亚纯函数,其零点与极点重级均≥m+1.如果对于F中的任意两个函数f,g,P(f)f′与P(g)g′分担h(z),则F在区域D内正规.该结果改进了Lei and Fang^([8]),Zhang^([16])等人的结果.
基金supported by National Natural Science Foundation of China(Grant No.10771076)Natural Science Foundation of Guangdong Province(Grant No.07006700)
文摘Let F be a family of functions meromorphic in a domain D,let P be a polynomial with either deg P≥3 or deg P=2 and P having only one distinct zero,and let b be a finite nonzero complex number.If,each pair of functions f and g in F,P(f)f and P(g)g share b in D,then F is normal in D.
