On uniqueness of \(L\)-functions in terms of zeros of strong uniqueness polynomial

Abhijit Banerjee; Arpita Kundu

doi:10.56754/0719-0646.2503.497

DOI:

https://doi.org/10.56754/0719-0646.2503.497

Abstract

In this article, we have mainly focused on the uniqueness problem of an \(L\)-function \(\mathcal{L}\) with an \(L\)-function or a meromorphic function \(f\) under the condition of sharing the sets, generated from the zero set of some strong uniqueness polynomials. We have introduced two new definitions, which extend two existing important definitions of URSM and UPM in the literature and the same have been used to prove one of our main results. As an application of the result, we have exhibited a much improved and extended version of a recent result of Khoai-An-Phuong [23]. Our remaining results are about the uniqueness of \(L\)-function under weighted sharing of sets generated from the zeros of a suitable strong uniqueness polynomial, which improve and extend some results in [12].

Keywords

Meromorphic function , strong uniqueness polynomial , uniqueness , shared sets , L function

Mathematics Subject Classification:

11M36 , 30D35

Abhijit Banerjee Department of Mathematics, University of Kalyani, West Bengal 741235, India. https://orcid.org/0000-0002-6160-7506
Arpita Kundu Department of Mathematics, University of Kalyani, West Bengal 741235, India.

Pages: 497–514
Date Published: 2023-12-30
Vol. 25 No. 3 (2023)

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