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The aim of this paper is to consider the value distribution of a differential monomial generated by a transcendental meromorphic function.

Complex Variables · Mathematics 2018-12-06 Bikash Chakraborty

In the existing literature, many researchers consider the uniqueness of the power of a meromorphic function with its derivative counterpart share certain values or small functions. Here we consider the same problem under the aegis of a more…

Complex Variables · Mathematics 2018-01-17 Abhijit Banerjee , Bikash Chakraborty

In this paper we have mainly focused on the uniqueness of two meromorphic functions under the realm of two shared sets problem with certain restrictions which in turn improve the results of { P. Sahoo and H. Karmakar, Uniqueness theorems…

Complex Variables · Mathematics 2020-09-01 Abhijit Banerjee , Saikat Bhattacharyya

In this paper, on the basis of a specific question raised in [6], we further continue our investigations on the uniqueness of a meromorphic function with its higher derivatives sharing two sets and answer the question affirmatively.…

Complex Variables · Mathematics 2018-01-08 Abhijit Banerjee , Bikash Chakraborty

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

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

This paper investigates the value distribution and growth properties of linear total differential polynomials $\mathcal{L}_k[D]f$ for meromorphic functions in several complex variables $\mathbb{C}^n$. By extending the classical Milloux…

Complex Variables · Mathematics 2026-01-22 Molla Basir Ahamed , Vasudevarao Allu

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

Starting with a question of Yuan-Li-Yi [Value distribution of L-functions and uniqueness questions of F. Gross, Lithuanian Math. J., 58(2)(2018), 249-262] we have studied the uniqueness of a meromorphic function f and an L-function L…

Number Theory · Mathematics 2020-08-28 Abhijit Banerjee , Arpita Kundu

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 investigate meromorphic solutions in $\mathbb{C}^m$ of the nonlinear differential equation \[\displaystyle f^n\partial_u(f)g^n\partial_u(g)=1,\] where $\partial_u(f)=\sum_{j=1}^mu_j\partial_j(f)$ and $\sum_{j=1}^m u_j\neq…

Complex Variables · Mathematics 2025-11-14 Abhijit Banerjee , Sujoy Majumder , Debabrata Pramanik , Nabadwip Sarkar

In this paper we study the distribution of the size of the value set for a random polynomial with degree at most $q-1$ over a finite field $\mathbb{F}_q$. We obtain the exact probability distribution and show that the number of missing…

Combinatorics · Mathematics 2014-07-23 Zhicheng Gao , Qiang Wang

In the context of several complex variables, we investigate the uniqueness problem for a power of a meromorphic function that shares a value with its $k$-th order directional derivative in $\mathbb{C}^m$. Our results extend previous…

Complex Variables · Mathematics 2025-11-04 Abjijit Banerjee , Sujoy Majumder , Debabrata Pramanik

This paper studies the uniqueness of two non-integral finite ordered meromorphic functions with finitely many poles when they share two finite sets. Also, studies an answer to a question posed by Gross for a particular class of meromorphic…

Complex Variables · Mathematics 2021-01-19 Bikash Chakraborty , Amit Kumar Pal , Sudip Saha , Jayanta Kamila

In this article, we construct explicit meromorphic solutions of first order linear $q$-difference equations in the complex domain and we describe the location of all their zeros and poles. The homogeneous case leans on the study of four…

Complex Variables · Mathematics 2023-07-04 Alberto Lastra , Pascal Remy

In the paper, we investigate the uniqueness problem of entire functions concerning their linear differential polynomial in shift and obtain three results which improve and generalize the recent result due to Qi (Ann. Polon. Math., 102…

Complex Variables · Mathematics 2025-12-03 Jeet Sarkar , Debabrata Pramanik

We study the effect of finite difference operators of finite order on the distribution of zeros of polynomials and entire functions.

Complex Variables · Mathematics 2018-07-06 Olga Katkova , Mikhail Tyaglov , Anna Vishnyakova

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

In this paper we prove a number of results concerning uniqueness of a meromorphic function as well as its derivative sharing one or two sets. In particular, we deal with the specific question raised in [18], [19], [20] and ultimately…

Complex Variables · Mathematics 2022-09-15 Abhijit Banerjee , Bikash Chakraborty

In this paper, we have investigated the uniqueness problems of entire and meromorphic functions concerning differential polynomials sharing a small function. Our results radically extended and improved the results of Bhoosnurmath-Pujari and…

Complex Variables · Mathematics 2019-07-01 Molla Basir Ahamed