On the magnitude of the least prime primitive root
type: Item
instance of: scholarly article
title: On the magnitude of the least prime primitive root
zbMATH Open document ID: 0712.11059
DOI: 10.1016/S0022-314X(05)80024-1
author: Leo Murata
published in: Journal of Number Theory
publication date: 1991-01-01T00:00:00Z
review text: The results of this paper are estimates (assuming the Generalised Riemann Hypothesis) for the least prime primitive root G(p) modulo a prime p. Thus the principal theorem is that if the GRH is true then for any monotone increasing function f satisfying \[ \lim_{x\to \infty}f(x)=\infty,\quad \exists A : f(x)\ll (\log x)^ A,\quad f(x)\ll f(x/\log x) \] the estimate \(G(p)\ll f(p)\) holds for all primes \(p<x\) with at most \(O(\pi (x)/\log f(x))\) exceptions. The method is a substantial extension of Hooley's proof (assuming GRH) of Artin's conjecture.
Mathematics Subject Classification ID: 11N64
Mathematics Subject Classification ID: 11A07
Mathematics Subject Classification ID: 11M26
Mathematics Subject Classification ID: 11R21
zbMATH DE Number: 4171045
zbMATH Keywords: Generalised Riemann Hypothesis
zbMATH Keywords: least prime primitive root
zbMATH Keywords: Artin's conjecture
reviewed by: D. R. B. Burgess
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4171045