Uniqueness of certain differential polynomial of L-functions and meromorphic functions sharing a polynomial

TL;DR

This paper establishes new sufficient conditions under which a meromorphic function and an L-function are related when they share a polynomial through a differential polynomial, extending previous uniqueness results.

Contribution

It introduces an improved main theorem that generalizes earlier results on the uniqueness of L-functions and meromorphic functions sharing differential polynomials.

Findings

Main theorem extends previous results on L-functions and differential polynomials.

Provides conditions for the uniqueness of functions sharing a polynomial.

Enhances understanding of the relation between meromorphic functions and L-functions.

Abstract

The purpose of this paper is to obtain some sufficient conditions to determine the relation between a meromorphic function and an L-function when certain differential polynomial generated by them sharing a one degree polynomial. The main theorem of the paper extends and improves all the results in {W. J. Hao and J. F. Chen, Uniqueness of L-functions concerning certain differential polynomials, Discrete Dyn. Nat. Soc., 2018, DOI. 10.1155/2018/4673165}, {F. Liu, X. M. Li and H. X. Yi, Value distribution of L-functions concerning shared values and certain differential polynomials, Proc. Japan. Acad. Ser. A, 93 (2017), 41-46} and {P. Sahoo and S. Haldar, Uniqueness results related to L-functions and certain differential polynomials, Tbilisi Math. J., 11(4) (2018), 67-78}.