Least primitive root and simultaneous power-non residues

2018/01/18 by Sartori, Andrea
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1801.06110

Abstract

Let p be a prime and let g(p) be the least primitive root modulo p. We prove that for any ε>0 and p large enough the bound g(p)≪ p^{(1)/(4√(e))+ε} holds for most prime p such that p-1 does not have small prime factors, but 2. We also give an explicit description of the exceptional set.

Related

• Square-full primitive roots
• The Least Square-free Primitive Root Modulo a Prime
• Topics In Primitive Roots
• Quadratic residues that are not primitive roots
• The smallest primitive root modulo a prime