Angular value distribution concerning shared values
Biao Pan, Wei-Chuan Lin
Abstract
Open-access reader
Biao Pan, Wei-Chuan Lin
Abstract
Open-access reader
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.
OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
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.
Key concepts: Meromorphic function, Mathematics, Complex plane, Order (exchange), Plane (geometry), Function (biology), Combinatorics, Distribution (mathematics)