Primitive Roots In Short Intervals

N. A. Carella

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arXiv · 1806.01150

Primitive Roots In Short Intervals

N. A. Carella

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Abstract

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

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BibTeX RIS

N. A. Carella. 2018-06-01. Primitive Roots In Short Intervals. https://arxiv.org/abs/1806.01150

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