Uniqueness of L-functions under weighted sharing of a set or a pair of sets
Samar HALDER
Received October 28, 2025. Published online March 24, 2026.
Abstract: The purpose of this paper is to study the uniqueness problem of an L-function $\mathcal{L}$ with another L-function or a nonconstant meromorphic function $f$ in the light of weighted sharing of a set or an ordered pair of sets, determined by the zeros of some polynomials. Using a generalized notion of set sharing and considering the most general form of the polynomial from which the shared set is generated, we have obtained several results that either extend or generalize certain results of Banerjee and Kundu (2023), Khoai, An, and Ninh, Khoai, An, and Phuong, Yuan, Li, and Yi, et al. In fact, owing to the generalized nature of the results, many applications are possible. In another result, we deal with uniqueness of $\mathcal{L}_1$ and $\mathcal{L}_2$, which extends a recent result due to Banerjee and Kundu (2024).
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Affiliations: Samar Halder, Department of Mathematics, JIS College of Engineering, P.O. Kalyani, Dist. Nadia - 741235, West Bengal, India, e-mail: samarhalder.mtmh@gmail.com
