Displaying similar documents to “Another algebraic proof of Weil's reciprocity”

Further investigations on a question of Zhang and Lü

Abhijit Banerjee, Bikash Chakraborty (2015)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Similarity:

In the paper based on the question of Zhang and Lü [15], we present one theorem which will improve and extend results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].

Normal families of bicomplex meromorphic functions

Kuldeep Singh Charak, Dominic Rochon, Narinder Sharma (2012)

Annales Polonici Mathematici

Similarity:

We introduce the extended bicomplex plane 𝕋̅, its geometric model: the bicomplex Riemann sphere, and the bicomplex chordal metric that enables us to talk about convergence of sequences of bicomplex meromorphic functions. Hence the concept of normality of a family of bicomplex meromorphic functions on bicomplex domains emerges. Besides obtaining a normality criterion for such families, the bicomplex analog of the Montel theorem for meromorphic functions and the fundamental normality...

Uniqueness of meromorphic functions sharing two finite sets

Jun-Fan Chen (2017)

Open Mathematics

Similarity:

We prove uniqueness theorems of meromorphic functions, which show how two meromorphic functions are uniquely determined by their two finite shared sets. This answers a question posed by Gross. Moreover, some examples are provided to demonstrate that all the conditions are necessary.

Unicity theorems for meromorphic functions that share three values

Wei-Ran Lü, Hong-Xun Yi (2003)

Annales Polonici Mathematici

Similarity:

We deal with the problem of uniqueness of meromorphic functions sharing three values, and obtain several results which improve and extend some theorems of M. Ozawa, H. Ueda, H. X. Yi and other authors. We provide examples to show that results are sharp.

Investigations on unique range sets of meromorphic functions in an angular domain

Sayantan Maity, Abhijit Banerjee (2023)

Mathematica Bohemica

Similarity:

We study unique range sets of meromorphic functions over an angular domain in the light of weighted sharing. One of our main results generalizes and improves a result of Xu et al. (2014). Most importantly, we have pointed out a gap in the proofs of some main results of Rathod (2021) and subsequently rectifying the gap we have conveniently improved the results.

Uniqueness of meromorphic functions sharing a meromorphic function of a smaller order with their derivatives

Xiao-Min Li, Hong-Xun Yi (2010)

Annales Polonici Mathematici

Similarity:

We prove some uniqueness theorems for meromorphic functions and their derivatives that share a meromorphic function whose order is less than those of the above meromorphic functions. The results in this paper improve those given by G. G. Gundersen & L. Z. Yang, J. P. Wang, J. M. Chang & Y. Z. Zhu, and others. Some examples are provided to show that our results are the best possible.

Uniqueness of meromorphic functions sharing three values

Indrajit Lahiri, Arindam Sarkar (2005)

Annales Polonici Mathematici

Similarity:

We prove a result on the uniqueness of meromorphic functions sharing three values with weights and as a consequence of this result we improve a recent result of W. R. Lü and H. X. Yi.

On meromorphic functions for sharing two sets and three sets inm-punctured complex plane

Hong-Yan Xu, Xiu-Min Zheng, Hua Wang (2016)

Open Mathematics

Similarity:

In this article, we study the uniqueness problem of meromorphic functions in m-punctured complex plane Ω and obtain that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 9, such that any two admissible meromorphic functions f and g in Ω must be identical if f, g share S1, S2 I M in Ω.

Exceptional values of meromorphic functions and of their derivatives on annuli

Yuxian Chen, Zhaojun Wu (2012)

Annales Polonici Mathematici

Similarity:

This paper is devoted to exceptional values of meromorphic functions and of their derivatives on annuli. Some facts on exceptional values for meromorphic functions in the complex plane which were established by Singh, Gopalakrishna and Bhoosnurmath [Math. Ann. 191 (1971), 121-142, and Ann. Polon. Math. 35 (1977/78), 99-105] will be considered on annuli.

The uniqueness of meromorphic functions ink-punctured complex plane

Hong Yan Xu, San Yang Liu (2017)

Open Mathematics

Similarity:

The main purpose of this paper is to investigate the uniqueness of meromorphic functions that share two finite sets in the k-punctured complex plane. It is proved that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 5, such that any two admissible meromorphic functions f and g in Ω must be identical if EΩ(Sj, f) = EΩ(Sj, g)(j = 1,2).