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2015 Angular value distribution concerning shared values
Biao Pan, Weichuan Lin
Rocky Mountain J. Math. 45(6): 1919-1935 (2015). DOI: 10.1216/RMJ-2015-45-6-1919

Abstract

In this paper, we investigate the number of sharing values of a meromorphic function and its derivative in one angular domain instead of the whole complex plane and obtain the following results: Let $f$ be a meromorphic function of lower order $>2$ in the complex plane. Then there exists a direction H: $\arg z=\theta \sb 0$ ($0\leq \theta _0\lt 2\pi $) such that for any positive number $\varepsilon $, $f$ and $f'$ share at most two distinct finite values without counting multiplicities in the angular region $ \{z: |\arg z-\theta _0|\lt \varepsilon \}$. This improve a result of Weichuan and Mori.

Citation

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Biao Pan. Weichuan Lin. "Angular value distribution concerning shared values." Rocky Mountain J. Math. 45 (6) 1919 - 1935, 2015. https://doi.org/10.1216/RMJ-2015-45-6-1919

Information

Published: 2015
First available in Project Euclid: 14 March 2016

zbMATH: 1356.30022
MathSciNet: MR3473162
Digital Object Identifier: 10.1216/RMJ-2015-45-6-1919

Subjects:
Primary: 30D35

Keywords: Angular distribution , meromorphic function , Shared Values

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

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Vol.45 • No. 6 • 2015
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