On the two conjectures
Complex Variables
2025-11-19 v1
Abstract
In this paper, we investigate the uniqueness problem of entire functions that share an entire function with their higher-order difference operators. We obtain two results that confirm the conjectures posed by Liu and Laine \cite{LL1} and by Zhang et al. \cite{ZKL1}, respectively. In addition, we present several relevant examples to further illustrate and support our findings
Cite
@article{arxiv.2511.13796,
title = {On the two conjectures},
author = {Nabadwip Sarkar and Debabrata Pramanik and Lata Mahato},
journal= {arXiv preprint arXiv:2511.13796},
year = {2025}
}