王辉坚, 孙道椿. 代数体函数的正规定理[J]. 华南师范大学学报(自然科学版), 2009, 1(2): 9-11 .
引用本文: 王辉坚, 孙道椿. 代数体函数的正规定理[J]. 华南师范大学学报(自然科学版), 2009, 1(2): 9-11 .
Sun Dao-chun, . NORMAL THEOREM OF ALGEBROIDAL FUNCTIONS[J]. Journal of South China Normal University (Natural Science Edition), 2009, 1(2): 9-11 .
Citation: Sun Dao-chun, . NORMAL THEOREM OF ALGEBROIDAL FUNCTIONS[J]. Journal of South China Normal University (Natural Science Edition), 2009, 1(2): 9-11 .

代数体函数的正规定理

NORMAL THEOREM OF ALGEBROIDAL FUNCTIONS

  • 摘要: 运用覆盖曲面的几何方法,证明了代数体函数族一个正规定理:设F为区\\域D内的一族k值代数体函数,且F的分支点是孤立的.若对\forall p\in D,总存在一\\个含于D内的邻域U(p),使得在U(p)内,对每个f_t\in F存在三个判别的复数 a_t1,\\a_t2,a_t3,满足\sum\limits_i=1^3\overlinen(U(p),a_ti,f_t)\leq 1,则F在D内正规.

     

    Abstract: By applying the main theorems on covering surface, a new normal criterion of algebroidal function was obtained. Let F be a family of k-valued algebroidal functions in a domain D of sphere V, and the branch points of F be isolated. If for all p\in D, there is a neighborhood U(p) such that for every f_t\in F, there exist three different complex values a_t1,a_t2,a_t3 satisfying \sum\limits_i=1^3\overlinen(U(p),a_ti,f_t)\leq 1, then F is normal in D.

     

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