2015Rocky Mountain Journal of MathematicsOpen access

Angular value distribution concerning shared values

Biao Pan, Wei-Chuan Lin

Open full text 4 citations

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.

Open-access reader

About this research paper

What this paper is about

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.

Why it matters

OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available 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.

Key concepts: Meromorphic function, Mathematics, Complex plane, Order (exchange), Plane (geometry), Function (biology), Combinatorics, Distribution (mathematics)

Related papers

Back to paper searchBrowse research topicsOriginal source
Angular value distribution concerning shared values — Research Paper | ScholarLens