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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 will establish a theorem concerning value distribution of L-functions in the Selberg class, which shows how an L-function and a meromorphic function are uniquely determined by their c-values and which, as a consequence, proves a result on the uniqueness of the Riemann zeta function. The results in this paper also extend the corresponding ones in Li 6. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we get two uniqueness theorems of meromorphic functions whose certain nonlinear differential polynomials share a polynomial. The results in this paper extend the corresponding results given by Fang (2002) in . Our reasoning in this paper will correct a defective reasoning in the proof of Theorem 4 in Bhoosnurmath and Dyavanal (2007) . An example is provided to show that some conditions of the main results in this paper are necessary. [Copyright &y& Elsevier]

In this paper, we prove some uniqueness theorems of entire functions and their derivatives that share an entire of function whose order is less than their order. The results in this paper improve those given by G. G. Gundersen and L. Z. Yang, J. P. Wang, J. M. Chang, and Y. Z. Zhu, X. M. Li and H. X. Yi, and others. Some examples are provided to show that the results in this paper are the best possible. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this article is to deal with the multiple values and uniqueness of meromorphic functions on annuli. We prove a general theorem on the multiple values and uniqueness of meromorphic functions on annuli, from which an analog of Nevanlinna’s famous five-value theorem is proposed. [Copyright &y& Elsevier]

Abstract: The main purpose of this paper is to investigate the uniqueness of transcendental meromorphic functions that share four values in one angular domain which is an unbounded subset of the whole complex plane. From one of our main results, a question of J.H. Zheng [J.H. Zheng, On uniqueness of meromorphic functions with shared values in one angular domain, Complex Var. Elliptic Equ. 48 (9) (2003) 777–785] is completely answered. Furthermore, we give an example to explain the necessity of the condition in our results. [Copyright &y& Elsevier]

Abstract: In this paper, we will prove some uniqueness theorems of meromorphic functions whose derivatives share four distinct small functions. The results in this paper improve those given by R. Nevanlinna, L. Yang, G.D. Qiu, and other authors. An example is provided to show that the results in this paper are best possible. [Copyright &y& Elsevier]

Abstract: In this paper, we deal with the problem of uniqueness and weighted sharing of two meromorphic functions with their first derivatives sharing a nonzero polynomial with the same multiplicities. The result in this paper improve those given by K. Tohge, Xiao-Min Li & Hong-Xun Yi, I. Lahiri & P. Sahoo. [Copyright &y& Elsevier]

Abstract: Using the idea of weighted sharing, we prove some results on uniqueness of meromorphic functions with three weighted sharing values. The results in this paper improve those given by H.X. Yi, T.C. Alzahary and H.X. Yi, T.C. Alzahary, I. Lahiri and N. Mandal, and other authors. [Copyright &y& Elsevier]

Abstract: In this paper, we deal with a uniqueness theorem of two meromorphic functions that have three weighted sharing values and one pair of values. The results in this paper improve those given by G.G. Gundersen, G. Brosch, T.C. Alzahary, T.C. Alzahary and H.X. Yi, I. Lahiri and P. Sahoo, and other authors. [Copyright &y& Elsevier]

Abstract: In this paper, we deal with a uniqueness theorem of two meromorphic functions that have three weighted sharing values and a sharing set with two elements. The results in this paper improve those given by G. Brosch, K. Tohge, T.C. Alzahary and H.X. Yi and other authors. [Copyright &y& Elsevier]

Abstract: A uniqueness theorem for two distinct non-constant meromorphic functions that share three values of finite weights is proved, which generalizes two previous results by H.X. Yi, and X.M. Li and H.X. Yi. As applications of it, many known results by H.X. Yi and P. Li, etc. could be improved. Furthermore, with the concept of finite-weight sharing, extensions on Osgood–Yang''s conjecture and Mues'' conjecture, and a generalization of some prevenient results by M. Ozawa and H. Ueda, ect. could be obtained. [Copyright &y& Elsevier]

Using the idea of weighted sharing, we prove some results on uniqueness of meromorphic functions sharing three values which improve some results given by H.-X. Yi, I. Lahiri, X. Hua and other authors. [Copyright &y& Elsevier]

Using the idea of weighted sharing of values, we study the problem of uniqueness of meromorphic functions that share three values. The results in this paper improve all theorems given by Lahiri in Nagoya Math. J. 161 (2001) 193–206. Examples are provided to show that some results in this paper are sharp. [Copyright &y& Elsevier]

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]

Abstract: In the paper, we study the uniqueness and the shared fixed-points of meromorphic functions and prove two main theorems which improve the results of Fang and Fang and Qiu. [Copyright &y& Elsevier]