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| DISTRIBUTION OF THE ${\boldkey (}{\boldkey 0},{\boldsymbol\infty}{\boldkey )}$ ACCUMULATIVE LINES OF MEROMORPHIC FUNCTIONS |
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Citation： |
Wu Shengjian.DISTRIBUTION OF THE ${\boldkey (}{\boldkey 0},{\boldsymbol\infty}{\boldkey )}$ ACCUMULATIVE LINES OF MEROMORPHIC FUNCTIONS[J].Chinese Annals of Mathematics B,1994,15(4):453~462 |
| Page view： 1150
Net amount： 892 |
Authors： |
Wu Shengjian; |
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| Abstract： |
Suppose that $f(z)$ is a meromorphic function of order $\la\, (0<\la<+\i)$
and of lower order $\mu$ in the plane. Let $\rho$ be a positive number such
that $\mu\le \rho\le\la.$
(1) If $f^{(l)}(z)\, (0\le l < +\i)$ has $p\, (1\le p<+\i)$ finite nonzero
deficient values $a_i\,(i=1,\cdots, p)$ with deficiencies $\delta(a_i,
f^{(l)})$, then $f(z)$ has a $(0,\i)$ accumulative line of order $\ge
\rho$ in any angular domain whose vertex is at the origin and whose magnitude is larger than
$$\max \left ({\frac \pi \rho},2\pi-{4\over \rho}\sum_{i=1}^p \arcsin
\sqrt{\frac {\delta(a_i,f^{(l)})} 2}\right ). $$
(2) If $f(z)$ has only $p\,(0 |
Keywords： |
Meromorphic function, Accumulative line, Order. |
Classification： |
32A20, 30D35. |
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