A fundamental theorem for algebroid function in $ k $-punctured complex plane

Hong Yan Xu; Yu Xian Chen; Jie Liu; Zhao Jun Wu; Hong Yan Xu; Yu Xian Chen; Jie Liu; Zhao Jun Wu

doi:10.3934/math.2021305

AIMS Mathematics

2021, Volume 6, Issue 5: 5148-5164. doi: 10.3934/math.2021305

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Research article

A fundamental theorem for algebroid function in $ k $-punctured complex plane

1.
School of Mathematics and Computer Science, Shangrao Normal University, Shangrao Jiangxi, 334001, P. R. China
2.
School of Mathematics and computer science, Xinyu University, Xinyu, Jiangxi, 338004, P. R. China
3.
School of Primary Education, Yuzhang Normal University, Nanchang Jiangxi 330103, P. R. China
4.
School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning 437100, P. R. China

Received: 04 January 2021 Accepted: 24 February 2021 Published: 10 March 2021
MSC : 32C20, 30D45

The main purpose of this article is to study the value distribution of algebroid function in the $ k $-punctured complex plane. We establish the second fundamental theorems for algebroid function concerning small algebroid functions in the $ k $-punctured complex plane, which extend the Nevanlinna theory for algebroid functions from single connected domain to multiple connected domain.
- algebroid function,
- $ k $-puncture plane,
- small algebroid function
Citation: Hong Yan Xu, Yu Xian Chen, Jie Liu, Zhao Jun Wu. A fundamental theorem for algebroid function in $ k $-punctured complex plane[J]. AIMS Mathematics, 2021, 6(5): 5148-5164. doi: 10.3934/math.2021305

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Abstract

The main purpose of this article is to study the value distribution of algebroid function in the $ k $-punctured complex plane. We establish the second fundamental theorems for algebroid function concerning small algebroid functions in the $ k $-punctured complex plane, which extend the Nevanlinna theory for algebroid functions from single connected domain to multiple connected domain.

References

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