关于模$p^\alpha$原根分布的推广

Extension on the Distribution of Primitive Roots Modulo $p$

中文关键词:  原根  三角和  Kloostermann和.

英文关键词:primitive root  trigonometric sums  Kloostermann sum.

中文摘要:

      设$p$为奇素数,$\alpha$为任意大于$1$的整数,对于任意给定的正整数$k$, $k|p^\alpha-p^{\alpha-1}$,本文主要研究模$p^\alpha$的$k$次剩余的分布性质.

英文摘要:

      Let $p$ be an odd prime. $k$ is a positive integer with $k|p^\alpha-p^{\alpha-1}$. The main purpose of this paper is to study the distribution of $k$-th residue modulo $p^\alpha$, when $\alpha$ is a positive integer with $\alpha>1$.