Uniqueness and two shared set problems of L-Function and certain class of meromorphic function

TL;DR

This paper investigates the uniqueness of meromorphic functions and L-functions sharing finite sets, identifies a flaw in prior work, and provides corrected results within this mathematical context.

Contribution

It addresses a key question on the uniqueness of L-functions and meromorphic functions sharing finite sets, correcting a significant error in previous research.

Findings

Identified a flaw in Sahoo-Halder's proof.

Rectified the results concerning sharing finite sets.

Enhanced understanding of L-function uniqueness.

Abstract

Starting with a question of Yuan-Li-Yi [Value distribution of L-functions and uniqueness questions of F. Gross, Lithuanian Math. J., 58(2)(2018), 249-262] we have studied the uniqueness of a meromorphic function f and an L-function L sharing two finite sets. At the time of execution of our work, we have pointed out a serious lacuna in the proof of a recent result of a of Sahoo-Halder [ Some results on L-functions related to sharing two finite sets, Comput. Methods Funct. Theo., 19(2019), 601-612] which makes most of the part of the Sahoo-Halder's paper under question. In context of our choice of sets, we have rectified Sahoo-Halder's result in a convenient manner.