Unicity on meromorphic function sharing three small functions CM with its higher-order difference operators

Abstract

In this paper, we study the uniqueness of the shift of meromorphic functions. We prove: Let $f$ be a non-constant meromorphic function satisfying ${\rho }_2(f)<1$, let $\eta$ be a non-zero complex number, and let $a,b,c\in \hat{S}(f)$ be three distinct small functions. If $f$ and ${\Delta }_{\eta }^{n}f$ share $a,b,c$ CM, then $f\equiv {\Delta }_{\eta }^{n}f$.

arXiv admin note: text overlap with arXiv:2009.08067