Unicity Theorems Concerning a L-Function and a Meromorphic Function

Inspired by a lot of studies on the uniqueness results of a L-function with a meromorphic function, in this article, we examine the uniqueness of two differential polynomials, one generated by a meromorphic function with finitely many poles and another by a L-function, when they share two values with some weight. The results of our examination extend, generalize as well as improve the results of Hao and Chen [2, 3].