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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…

Complex Variables · Mathematics 2021-12-28 Ta Thi Hoai An , Nguyen Viet Phuong

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…

Complex Variables · Mathematics 2019-02-27 Si Duc Quang

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…

Number Theory · Mathematics 2012-05-01 Mathilde Herblot

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…

Complex Variables · Mathematics 2021-02-08 Bikash Chakraborty , Jayanta Kamila , Amit Kumar Pal , Sudip Saha

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.

Complex Variables · Mathematics 2022-09-14 Abhijit Banerjee , Bikash Chakraborty

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…

Complex Variables · Mathematics 2025-10-28 Abhijit Banerjee , Sujoy Majumder , Nabadwip Sarkar

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…

Complex Variables · Mathematics 2023-05-08 Kiyoshi Takeuchi

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…

Complex Variables · Mathematics 2020-10-26 Janne Heittokangas , Jun Wang , Zhi-Tao Wen , Hui Yu

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…

Number Theory · Mathematics 2011-05-31 Kamal Boussaf , Escassut Alain , Jacqueline Ojeda

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.

Complex Variables · Mathematics 2017-05-11 Abhijit Banerjee , Sujoy Majumder , Bikash Chakraborty

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.

Complex Variables · Mathematics 2022-06-08 Zhiguo Ding , Michael E. Zieve

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…

Complex Variables · Mathematics 2016-10-03 J. W. Osborne , D. J. Sixsmith

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.…

Complex Variables · Mathematics 2023-08-01 Si Duc Quang

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…

Algebraic Geometry · Mathematics 2018-03-29 Mihai Tibar

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…

Complex Variables · Mathematics 2008-10-06 Josip Globevnik

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…

Combinatorics · Mathematics 2007-05-23 Dmitri Panov , Dimitri Zvonkine

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…

Complex Variables · Mathematics 2025-12-22 Sanjay Mallick , Ripan Saha

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…

Number Theory · Mathematics 2020-08-26 Abhijit Banerjee , Arpita Kundu

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,…

Complex Variables · Mathematics 2022-04-17 XiaoHuang Huang

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.

Complex Variables · Mathematics 2018-07-26 J. K. Langley