Journal of the
Korean Mathematical Society JKMS

Let $f(z)$ be a meromorphic function in several variables satisfying $$\limsup\limits_{r\rightarrow\infty}\frac{\log T(r,f)}{r}=0.$$ We mainly investigate the uniqueness problem on $f$ in $\mathbb{C}^{m}$ sharing polynomial or periodic small function with its difference polynomials from a new perspective. Our main theorems can be seen as the improvement and extension of previous results.

Keywords: Meromorphic function, uniqueness, difference polynomials, periodic small function, several variables

MSC numbers: Primary 32H30, 32A20, 30D35

Supported by: This work was financially supported by the National Natural Science Foundation of China (Grant Nos.12171050, 12071047) and the Fundamental Research Funds for the Central Universities (Grant No.500421126).