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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-functions L 1 and L 2 satisfy the same functional equation with a (1) = 1 and L 1 − 1 (c j) = L 2 − 1 (c j) for two distinct finite complex numbers c 1 and c 2 , then L 1 = L 2. We prove that if two L-functions L 1 and L 2 have positive degree and satisfy the same functional equation with a (1) = 1 and E L 1 (S) = E L 2 (S) for a finite set S = { c 1 , c 2 , c 3 } , where c 1 , c 2 and c 3 are three distinct finite complex values, then L 1 = L 2. 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)]. [ABSTRACT FROM AUTHOR]

We study the value distribution of L-functions and uniqueness questions of meromorphic functions sharing one or two sets with L-functions. The results in this paper extend the corresponding results from [J. Steuding, Value Distribution of L-Functions, Lect. Notes Math., Vol. 1877, Springer-Verlag, Berlin, Heidelberg, 2007, p. 152] and [B.Q. Li, A result on value distribution of L-functions, Proc. Am. Math. Soc., 138(6):2071-2077, 2010]. The studied questions in this paper are related to the questions of Gross from [F. Gross, Factorization of meromorphic functions and some open problems, in Complex Analysis, Kentucky 1976. Proceedings of the Conference Held at the University of Kentucky, May 18-22, 1976, Lect. Notes Math., Vol. 599, Springer-Verlag, Berlin, Heidelberg, 1977, pp. 51-69]. Here the meromorphic functions are of finitely many poles in the complex plane. [ABSTRACT FROM AUTHOR]

We use Zalcman’s lemma to study a uniqueness question for meromorphic functions where certain associated nonlinear differential polynomials share a nonzero value. The results in this paper extend Theorem 1 in Yang and Hua [‘Uniqueness and value-sharing of meromorphic functions’, Ann. Acad. Sci. Fenn. Math. 22 (1997), 395–406] and Theorem 1 in Fang [‘Uniqueness and value sharing of entire functions’, Comput. Math. Appl. 44 (2002), 823–831]. Our reasoning in this paper also corrects a defect in the reasoning in the proof of Theorem 4 in Bhoosnurmath and Dyavanal [‘Uniqueness and value sharing of meromorphic functions’, Comput. Math. Appl. 53 (2007), 1191–1205]. [ABSTRACT FROM PUBLISHER]

We study the value distribution of L-functions and uniqueness questions of meromorphic functions sharing one or two sets with L-functions. The results in this paper extend the corresponding results from [J. Steuding, Value Distribution of L-Functions, Lect. Notes Math., Vol. 1877, Springer-Verlag, Berlin, Heidelberg, 2007, p. 152] and [B.Q. Li, A result on value distribution of L-functions, Proc. Am. Math. Soc., 138(6):2071-2077, 2010]. The studied questions in this paper are related to the questions of Gross from [F. Gross, Factorization of meromorphic functions and some open problems, in Complex Analysis, Kentucky 1976. Proceedings of the Conference Held at the University of Kentucky, May 18-22, 1976, Lect. Notes Math., Vol. 599, Springer-Verlag, Berlin, Heidelberg, 1977, pp. 51-69]. Here the meromorphic functions are of finitely many poles in the complex plane. [ABSTRACT FROM AUTHOR]