Dirichlet series satisfying a Riemann type functional equation and sharing one set

Abstract

In 2011, Li [A uniqueness theorem for Dirichlet series satisfying a Riemann type functional equation. Adv Math. 2011;226(5):4198–4211] proved that if two L-functions and satisfy the same functional equation with and for two distinct finite complex numbers and then We prove that if two L-functions and have positive degree and satisfy the same functional equation with and for a finite set where and are three distinct finite complex values, then The main results of this paper are concerning some questions posed by Gross [Factorization of meromorphic functions and some open problems. Complex Analysis, Kentucky 1976 (Proc.Conf.); Berlin: Springer-Verlag; 1977. p. 51–69. (Lecture Notes in Mathematics; 599)].