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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 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: In this paper, we prove a theorem on the regular growth of the solutions of a linear differential equation, as an application of which we obtain some uniqueness theorems of an entire function sharing a finite nonzero complex number with its th derivative and a linear differential polynomial of its th derivative under the restriction of finite lower order or of finite lower hyper-order that is not a positive integer. The results in this paper improve many known results. Some examples are provided to show that the results in this paper are the best possible. [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]

Abstract: In this paper, we study the growth of solutions of a first-order linear differential equation and that of a second-order linear differential equation. From this we obtain some uniqueness theorems of a nonconstant entire function and its first derivative having the same fixed points with the same multiplicities. The results in this paper also improve some known results. Some examples show that the results in this paper are best possible. [Copyright &y& Elsevier]

Abstract: In this paper, we give the definition of iterated order to classify functions of fast growth in the unit disc, and investigate the growth of solutions of linear differential equations with analytic coefficients of iterated order in the unit disc. We obtain several results concerning the iterated order of solutions. [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]

Let f be a nonconstant entire function, and let k (⩾2) be an integer. We denote by Ef(z)={z∈C: f(z)=z, counting multiplicities} the set consisting of all the fixed points of f. This paper proves that if f and f′ have the same fixed points, namely, Ef(z)=Ef′(z), and if f(k)(z)=z whenever f(z)=z, then f≡f′. [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]

This paper studies the uniqueness problem on entire function that share a finite, nonzero value CM with their derivatives and proves two main theorems which generalize some results given by Jank, Mues and Volkmann, P. Li and C.C. Yang, H.L. Zhong etc. An example shows that the condition of one of our theorems is necessary. [Copyright &y& Elsevier]

In this paper, we prove that if a nonconstant finite order meromorphic function f and its n-th order difference operator Δ η n f share a 1 , a 2 , a 3 CM, where n is a positive integer, η ≠ 0 is a finite complex value, and a 1 , a 2 , a 3 are three distinct finite complex values, then f (z) = Δ η n f (z) for each z ∈ C. The main results in this paper improve and extend many known results concerning a conjecture posed by Chen and Yi in 2013. [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]

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]

Abstract: This paper studies the uniqueness problem on entire function that share a finite, nonzero value with their linear differential polynomials and proves some theorems which generalize some results given by Jank, Mues and Volkmann, P. Li, J.P. Wang and H.X. Yi. [Copyright &y& Elsevier]