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The paper develops an equidistribution theory of meromorphic mappings from a complete K\"ahler manifold with non-negative Ricci curvature into a complex projective manifold intersecting normal crossing divisors. When the domain manifolds…

Complex Variables · Mathematics 2025-01-22 Xianjing Dong

The purpose of this paper has twofold. The first is to establish a second main theorem for meromorphic functions on annuli and meromorphic function targets (may not be small functions) with truncated counting functions (truncation level 1)…

Complex Variables · Mathematics 2023-06-27 Si Duc Quang

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

The main goal of this paper is to establish the higher-dimensional Nevanlinna theory in tropical geometry. We first develop a theory of tropical meromorphic functions ( holomorphic maps) in several variables, such as the proximity function,…

Algebraic Geometry · Mathematics 2025-08-29 Tingbin Cao , Jiahu Peng

We describe some results of value distribution theory of holomorphic curves and quasiregular maps, which are obtained using potential theory. Among the results discussed are: extensions of Picard's theorems to quasiregular maps between…

Complex Variables · Mathematics 2007-05-23 Alexandre Eremenko

In this research notes, we investigate some remain problems in the uniqueness of meromorphic function. Using some deep results of Yamanoii, we obtain some results in this notes.

Complex Variables · Mathematics 2025-03-18 Xiaohuang Huang

The subject of our thesis is the uniqueness theory of meromorphic functions and it is devoted to problems concerning Bruck conjecture, set sharing and related topics. The tool, we used in our discussions is classical Nevanlinna theory of…

Complex Variables · Mathematics 2017-11-27 Bikash Chakraborty

We give an elementary characterization of rational functions among meromorphic functions in the complex plane.

Complex Variables · Mathematics 2017-12-13 Bao Qin Li

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

Nevanlinna theory studies the value distribution of meromorphic functions and provides powerful results in the form of the First and Second Main Theorems. In this paper, we introduce quaternionic analogues of the Nevanlinna functions.…

Complex Variables · Mathematics 2026-03-23 Muhammad Ammar

We give a short survey on generalizations of Nevanlinna's theorems on zero distribution of bounded holomorphic functions and representation of meromorphic functions in multiply connected domains. It is a part of our report in the conference…

Complex Variables · Mathematics 2011-04-28 Bulat N. Khabibullin

We characterize meromorphic function fields closed by partial derivatives in n variables.

Complex Variables · Mathematics 2019-07-09 Yukitaka Abe

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

In this note, we introduce a new kind of pair of finite range sets in $\mathbb{C}$ for meromorphic functions corresponding to their uniqueness, i.e., how two meromorphic functions are uniquely determined by their two finite shared sets.

Complex Variables · Mathematics 2023-11-21 Amit Kumar Pal , Bikash Chakraborty , Sudip Saha

In this paper, we give a simple proof and strengthening of a uniqueness theorem of meromorphic functions which partially share 0, $\infty$ CM and 1 IM with their difference operators. Meanwhile, we partial solve a conjecture given by…

Complex Variables · Mathematics 2021-01-05 Feng Lü , Zhenliu Yang

Scalar-valued meromorphic Herglotz-Nevanlinna functions are characterized by the interlacing property of their poles and zeros together with some growth properties. We give a characterization of matrix-valued Herglotz-Nevanlinna functions…

Complex Variables · Mathematics 2022-05-02 Jakob Reiffenstein

In this paper, we investigate the uniqueness property of meromorphic functions together with its linear difference polynomial sharing two sets. Using the polynomial introduced in [FILOMAT 33(18)(2019), 6055-6072], we have improved the…

Complex Variables · Mathematics 2020-09-29 Goutam Haldar

Let $f$ be a meromorphic function on the complex plane $\mathbb C$ with the maximum function of its modulus $M(r,f)$ on circles centered at zero of radius $r$. A number of classical, well-known and widely used results allow us to estimate…

Complex Variables · Mathematics 2021-04-16 B. N. Khabibullin

We show that it is possible to approximate the zeta-function of a curve over a finite field by meromorphic functions which satisfy the same functional equation and moreover satisfy (respectively do not satisfy) the analogue of the Riemann…

Complex Variables · Mathematics 2010-08-04 P. M. Gauthier , N. Tarkhanov

It is an expanded form of Drasin's work on normality of family of meromorphic functions given in his seminal paper titled "Normal Families and the Nevanlinna Theory".

Complex Variables · Mathematics 2018-10-17 Manisha Saini