UNIQUENESS RESULTS RELATED TO L-FUNCTIONS SATISFYING SAME FUNCTIONAL EQUATION UNDER SHARING PRE-IMAGES OF RANGE SETS

Abstract

In this article we have studied the uniqueness problem of L-function L in extended-Selberg class with some meromorphic function f having finitely many poles, when the pre-image of a set with respect to L coincides with the same of another set with respect to f. We have studied the problem corresponding to two Selberg class L-functions as well. With the new notion of sharing which is the generalization of the definition of traditional set sharing, we have significantly improved the results of [ Houston. J. Math., 46(4)(2020), 915-923], and some of [Complex Var. Elliptic Equ., Published online (DOI: 10.1080/17476933.2022.2069759)]. In another result, we have extended a result of [Ann. Polon. Math., 126(2021), 265-278] which in turn provid the best possible answer to a question raised in the same paper.