A NOTE TO THE NEVANJUNNA'S FUNDAMENTAL THEOREM |
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Authors: | Zhong Changyong |
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Institution: | Department of Mathematics, Sichuan University, Chengdu, Sichuan, China. |
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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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Keywords: | |
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