Bulletin of the Iranian Mathematical Society

, Volume 44, Issue 1, pp 19–41

# Meromorphic Functions Having the Same Inverse Images of Four Values on Annuli

Original Paper

## Abstract

In this paper, we extend and improve the four-value theorems of Nevanlinna and Fujimoto to the case of meromorphic functions on the annuli. For detail, we will prove that there are at most two admissible meromorphic functions on an annulus sharing a value with multiplicities truncated by two and other three values regardless of multiplicities. We also show that if four admissible meromorphic functions on an annulus share four values regardless of multiplicities then two of them must coincide. Moreover, in our result, the inverse images of these values by the functions with multiplicities more than a certain number do not need to be counted.

## Keywords

Meromorphic function Nevanlinna theory Annulus

## Mathematics Subject Classification

Primary 30D35 Secondary 32H30

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© Iranian Mathematical Society 2018

## Authors and Affiliations

• Si Duc Quang
• 1
• 2
• Tran An Hai
• 3
• Nguyen Thi Thanh Hien
• 4
• Ha Huong Giang
• 5
1. 1.Department of MathematicsHanoi National University of EducationHanoiVietnam
2. 2.Thang Long Institute of Mathematics and Applied SciencesHanoiVietnam
3. 3.Division of MathematicsBanking AcademyHanoiVietnam
4. 4.Department of MathematicsUniversity of Hanoi Textile IndustryHanoiVietnam
5. 5.Faculty of Fundamental SciencesElectric Power UniversityHanoiVietnam