Related papers: Meromorphic functions on annuli sharing finite set…
In this paper, we establish a new second main theorem for meromorphic functions on a non-Archimedean field and small functions with counting functions truncated to level $1.$ As an application, we show that two meromorphic functions on a…
In this article, we establish some new second main theorems for meromorphic mappings of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ and moving hyperplanes with truncated counting functions. Our results are improvements of the previous…
The classic Schneider-Lang theorem in transcendence theory asserts that there are only finitely many points at which algebraically independent complex meromorphic functions of finite order of growth can simultaneously take values in a…
In this paper, we exhibit the equivalence between different notions of unique range sets, namely, unique range sets, weighted unique range sets and weak-weighted unique range sets under certain conditions.\par Also, we present some…
In the paper, we introduce a new type of unique range set for meromorphic function having deficient values which will improve all the previous result in this aspect.
The objective of the paper is twofold. The first objective is to study the uniqueness problem of meromorphic function $f(z)$ when $f^{(1)}(z)$ shares two distinct finite values $a_1$, $a_2$ and $\infty$ CM with $\Delta_cf(z)$. In this…
We define Bernstein-Sato polynomials for meromorphic functions and study their basic properties. In particular, we prove a Kashiwara-Malgrange type theorem on their geometric monodromies, which would be useful also in relation with the…
The $\varphi$-order was introduced in 2009 for meromorphic functions in the unit disc, and was used as a growth indicator for solutions of linear differential equations. In this paper, the properties of meromorphic functions in the complex…
Let K be a complete algebraically closed p-adic field of characteristic zero. Let f, g be two transcendental meromorphic functions in the whole field K or meromorphic functions in an open disk that are not quotients of bounded analytic…
In this paper, we prove some uniqueness theorems concerning the derivatives of meromorphic functions when they share three sets. The obtained results improve some recent existing results.
We prove a new bound on the number of shared values of distinct meromorphic functions on a compact Riemann surface, explain a mistake in a previous paper on this topic, and give a survey of related questions.
We study the class $\mathcal{M}$ of functions meromorphic outside a countable closed set of essential singularities. We show that if a function in $\mathcal{M}$, with at least one essential singularity, permutes with a non-constant rational…
The purpose of this article is twofold. The first is to prove a second main theorem for meromorphic mappings of $\C^m$ into a complex projective variety intersecting hypersurfaces in subgeneral position with truncated counting functions.…
We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of…
Let D be a bounded domain in the complex plane whose boundary bD consists of finitely many pairwise disjoint real analytic simple closed curves. Let f be an integrable function on bD. In the paper we show how to compute the candidates for…
We study the number of meromorphic functions on a Riemann surface with given critical values and prescribed multiplicities of critical points and values. When the Riemann surface is $\CP^1$ and the function is a polynomial, we give an…
In the paper, concerning a question of Yi [23], we study general criterion for the uniqueness of an L-function and a general meromorphic function. Our results improve and extend all the existing results in this direction [23, 18, 17, 4] to…
The purpose of the paper is to study the uniqueness problem of a $L$ function in the Selberg class sharing one or two sets with an arbitrary meromorphic function having finite poles. We manipulate the notion of weighted sharing of sets to…
In this paper, we study the uniqueness of the differential-difference of meromorphic functions. We prove the following result: Let $f$ be a nonconstant meromorphic function of $\rho_{2}(f)<1$, let $\eta$ be a non-zero complex number,…
In this note it is shown that two key results on transcendental singularities for meromorphic functions of finite lower order have refinements which hold under the weaker hypothesis that the logarithmic derivative has finite lower order.