设$p$为奇素数, $n$, $k$为满足$\frac{n}{e}$为奇数的正整数, 其中$e=\mathrm{g}\mathrm{c}\mathrm{d}(n,k)$. 文章研究一类幂函数在${\mathbb{F}}_{p^n}$上的差分谱, 其指数$d$满足同余方程$d(p^k+1)\equiv 2(\mathrm{m}\mathrm{o}\mathrm{d}{p}^n-1)$. 这类指数将Sung-Tai Choi等人(2013)研究的幂函数所对应的两类指数进行了统一和推广.} \Keywords{差分谱; 幂函数; 分圆数; 有限域

Let $p$ be an odd prime and $n$, $k$ be integers such that $\frac{n}{e}$ is odd, where $e=\mathrm{g}\mathrm{c}\mathrm{d}(n,k)$. In this paper, we determine the differential spectrums for a class of power functions over ${\mathbb{F}}_{p^n}$ with the exponent $d$ satisfying $d(p^k+1)\equiv 2(\mathrm{m}\mathrm{o}\mathrm{d}{p}^n-1)$. These exponents are the unification and generalization of the two class of exponents investigated by Sung-Tai Choi, et al. (2013).