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| A NOTE TO THE NEVANJUNNA'S FUNDAMENTAL THEOREM |
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Citation： |
Zhong Changyong.A NOTE TO THE NEVANJUNNA'S FUNDAMENTAL THEOREM[J].Chinese Annals of Mathematics B,1989,10(3):351~360 |
| Page view： 892
Net amount： 813 |
Authors： |
Zhong Changyong; |
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| Abstract： |
In this paper, the author extends Nevanlinna's second fundamental theorem and establishes the following inequality:
Let $\[p(s,u) = {A_v}(s){u^v} + {A_1}(s){u^{v - 1}} + \cdots + {A_0}(s)\]$
be an irreducible two-variable polynomial and $f(s)$ a transcendental entire function, then
$$\[(\nu - 1)T(r,f) < N(r,\frac{1}{{p(z,f(z))}}) + S(r,f)\]$$
with
$$\[S(r,f) = O(\log (rT(r,f)))n.e\]$$
where an. "n.e" means that the estimation holds for all large r with possibly an exceptional of finite measure when f is of infinite order. |
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