English

The smallest primitive root modulo a prime

Number Theory 2018-03-30 v1

Abstract

In this paper we will consider new bounds on the smallest primitive root modulo a prime. We will make more judicious use of the P\`olya--Vinogradov and Burgess inequalities, and use them to prove that the smallest primitive root is smaller than p0.68p^{0.68} for all primes pp.

Cite

@article{arxiv.1803.11061,
  title  = {The smallest primitive root modulo a prime},
  author = {Jana Pretorius},
  journal= {arXiv preprint arXiv:1803.11061},
  year   = {2018}
}

Comments

8 pages

R2 v1 2026-06-23T01:08:48.970Z