The unique range set of meromorphic functions in an angular domain

Area of Science:

• Complex Analysis
• Meromorphic Functions
• Number Theory

Background:

• Uniqueness problems are central to the theory of meromorphic functions.
• Previous research established unique range sets for specific domains.
• Angular domains present unique challenges due to their unbounded nature.

Purpose of the Study:

• To investigate the uniqueness of meromorphic functions in an angular domain.
• To extend existing unique range set theorems to a broader class of domains.
• To introduce a novel shared set for uniqueness problems.

Main Methods:

• Utilizing Tsuji's characteristic method.
• Applying Nevanlinna's value distribution theory.
• Analyzing the properties of the newly defined shared set.

Main Results:

• Established new conditions for the uniqueness of meromorphic functions in angular domains.
• Demonstrated that the uniqueness results are sharp.
• Provided examples illustrating the significance of the new shared set.

Conclusions:

• The findings contribute to a deeper understanding of uniqueness problems in complex analysis.
• The results generalize and improve upon existing theorems.
• The study opens avenues for further research into shared values in angular domains.