The linear dependency of L−functions and meromorphic functions sharing finite sets

Abstract

In this paper we investigate the linear dependency of L functions and meromorphic functions sharing finite sets. As a consequence, we present some classes of subsets S,T in C such that for a meromorphic function f and an L-function L, the condition that f and L share S and T, respectively (counting multiplicity) implies f = hL for a non-zero constant h. We discuss some applications of main result. The main result obtained in this paper improves and extends a recent result due to the authors in [32]. We extend previous results of Yuan, Li and Yi [32] by considering distinct finite sets S,T and establishing linear dependency between f and L. Our results are inspired by a work of Yuan, Li, and Yi in [32] and Khoai et al. in [11] and [13].