Primitive Roots In Short Intervals

Abstract

Let $p\ge 2$ be a large prime, and let $N\gg (\log p{)}^{1+\epsilon }$. This note proves the existence of primitive roots in the short interval $[M,M+N]$, where $M\ge 2$ is a fixed number, and $\epsilon >0$ is a small number. In particular, the least primitive root $g(p)=O\left((\log p{)}^{1+\epsilon }\right)$, and the least prime primitive root $g^{\ast }(p)=O\left((\log p{)}^{1+\epsilon }\right)$ unconditionally.

Twenty Eight Pages. Keywords: Least primitive root, Least prime primitive root, Primitive root in short interval

References in corpus (1)

• Least Prime Primitive Roots

Cited by in corpus (1)

• Configurations Of Consecutive Primitive Roots