Let f be a nonconstant meromorphic function in the complex plane C. We shall use the standard notations in Nevanlinna’s value distribution theory of meromorphic functions such as T r, f , N r, f , and m r, f see, e.g., 1, 2 . The notation S r, f is defined to be any quantity satisfying S r, f o T r, f as r → ∞ possibly outside a set of E of finite linear measure. Let F be a family of meromorphi...

In this paper, we shall study the uniqueness problems of meromorphic functions of differential polynomials sharing two values IM. Our results improve or generalize many previous results on value sharing of meromorphic functions.

We prove extension results for meromorphic functions by combining the Kohn-Rossi extension theorems with Andreotti's theory on the algebraic and analytic dependence of meromorphic functions on pseudoconcave manifolds. Versions of Kohn-Rossi theorems for pseudo-convex domains are included.

Laplace operators perturbed by meromorphic potential on the Riemann and separated type Klein surfaces are constructed and their indices are calculated by two different ways. The topological expressions for the indices are obtained from the study of spectral properties of the operators. Analytical expressions are provided by the Heat Kernel approach in terms of the functional integrals. As a res...

We determine all cases when there exists a meromorphic solution of the ODE νw + bw + μw + w/2 +A = 0. This equation describes traveling waves solutions of the KuramotoSivashinsky equation. It turns out that there are no other meromorphic solutions besides those explicit solutions found by Kuramoto and Kudryashov. The general method used in this paper, based on Nevanlinna theory, is applicable t...

In this paper, we first obtain the famous Xiong Inequality of meromorphic functions on annuli. Next we get a uniqueness theorem of meromorphic function on annuli concerning to their multiple values and derivatives by using the inequality.

In the paper we compare the relative Valiron defect with the relative Nevanlinna defect of a meromorphic function or a transcendental meromorphic function on the basis of sharing of values of them. Mathematics Subject Classification: 30D35, 30D30

We introduce and study some classes of meromorphic functions defined by using a meromorphic analogue of Noor [also Choi-Saigo-Srivastava] operator for analytic functions. Several inclusion results and some other interesting properties of these classes are investigated.

We consider the relationship between the conjectured uniqueness of the Moonshine Module, V♮, and Monstrous Moonshine, the genus zero property of the modular invariance group for each Monster group Thompson series. We first discuss a family of possible Zn meromorphic orbifold constructions of V♮ based on automorphisms of the Leech lattice compactified bosonic string. We reproduce the Thompson se...

This is an appendix to the English translation of the book by A. A. Goldberg and I. V. Ostrovskii, Distribution of values of meromorphic functions, Moscow, Nauka, 1970. An English translation of this book is to be published soon by the AMS. In this appendix we survey the results obtained on the topics of the book after 1970. The literature on meromorphic functions is very large. There is a comp...