利用复分析的值分布理论研究了亚纯函数的唯一性,给出了下面的结果.设q(z)为k次有理函数,f(z)和g(z)是两个超越亚纯函数, fg与q没有共同的极点. n是正整数且n≥max{11,k+1}. 如果fn(z)f'(z), gn(z)g'(z)分担有理函数q(z) CM, 则 f(z)=c1ec∫q(z)dz,g(z)=c2e-c∫q(z)dz, 这里c1,c2 和c是三个常数且满足 (c1c2)n+1c2=-1; 或者f(z)≡tg(z),其中t是一个常数满足tn+1=1.
Abstract
We use the theory of value distribution and study the uniqueness of meromorphic functions. We will prove the following result: Let q(z) be a rational function of degree k, f(z) and g(z) be two transcendental meromorphic functions, and let q have no same poles as fg, n be a positive integer and n ≥ max{11, k + 1}. If fn(z)f'(z) and gn(z)g'(z) share q(z) CM, then either f(z) = c1ec∫q(z)dz, g(z) = c2e-c∫q(z)dz, where c1, c2 and c are three constants satisfying (c1c2)n+1c2 = -1, or f(z) ≡ tg(z) for a constant t such that tn+1 = 1.
关键词
亚纯函数 /
有理函数 /
零点 /
极点
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Key words
meromorphic function /
rational function /
zero point /
pole point
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参考文献
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脚注
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