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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-functionsandsatisfy the same functional equation withandfor two distinct finite complex numbersandthenWe prove that if two L-functionsandhave positive degree and satisfy the same functional equation withandfor a finite setwhereandare three distinct finite complex values, thenThe 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)].

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