Affordable Access

Publisher Website

On the least prime primitive root

Authors
Journal
Journal of Number Theory
0022-314X
Publisher
Elsevier
Volume
133
Issue
11
Identifiers
DOI: 10.1016/j.jnt.2013.05.007
Keywords
  • Primitive Root
  • L-Function
Disciplines
  • Mathematics

Abstract

Abstract We study the uniform upper bound for the least prime that is a primitive root. Let g⁎(q) be the least prime primitive root (mod q) where q is a prime power or twice a prime power of a prime p. The upper bound for g⁎(q) is studied by many authors who succeeded in establishing various conditional upper bounds. However, no uniform bounds were known other than Linnikʼs bound on the least prime in an arithmetic progression. In this paper, we prove that g⁎(q)≪p3.1. The exponent 3.1 is improved from the known exponent 4.5 from Linnikʼs bound for the prime modulus.

There are no comments yet on this publication. Be the first to share your thoughts.