Uniqueness of an entire function sharing two values jointly with its differential polynomials

2021/07/12 by Haldar, Goutam
#30D35 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.05705

Abstract

In this paper, we continue to investigate the uniqueness problem when an entire function f and its linear differential polynomial L(f) share two distinct complex values CMW (counting multiplicities in the weak sense) jointly. Also, We investigate the same problem when f and its differential monomial M(f) share two distinct complex values CMW. Our results generalize the recent result of Lahiri (Comput. Methods Funct. Theory, https://doi.org/10.1007/s40315-020-00355-4).

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• Uniqueness of differential polynomials sharing one value
• Partial sharing and cross sharing of entire function with its derivative
• Uniqueness of entire functions concerning their linear differential polynomials in shift
• Value sharing by an entire function with its derivatives
• Uniqueness of entire functions concerning differential-difference polynomials sharing small functions