Partial sharing and cross sharing of entire function with its derivative

2025/09/24 by Majumder, Sujoy, Sarkar, Nabadwip, Pramanik, Debabrata
#30D35 #30D45 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.20273

Abstract

In the paper, we investigate the uniqueness problem of a power of an entire function that share one value partially with it's linear differential polynomial and obtain a result, which improves several previous results in a large scale. Also in the paper we include some applications of our main result. Moreover, we solve the question raised by Wang and Liu (Value cross-sharing of meromorphic functions, Comput. Methods Funct. Theory (2023). https://doi.org/10.1007/s40315-023-00481-9) for a special case related to value cross-sharing.

Citations

• Normal families and uniqueness of entire functions and their derivatives
• GENERALIZED LOGARITHMIC DERIVATIVE ESTIMATES OF GOL'DBERG–GRINSHTEIN TYPE
• On deficiencies of differential polynomials, II

Related

• Uniqueness of an entire function sharing two values jointly with its differential polynomials
• Relationship between the value-sharing behavior of an entire function and its derivative, and the analytic structure of a nonlinear differential equation
• Value sharing by an entire function with its derivatives
• Uniqueness of differential polynomials sharing one value
• Meromorphic functions that partially share values with their first derivative