Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415551 | Journal of Number Theory | 2013 | 25 Pages |
Abstract
We study the uniform upper bound for the least prime that is a primitive root. Let gâ(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 gâ(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 gâ(q)âªp3.1. The exponent 3.1 is improved from the known exponent 4.5 from Linnikʼs bound for the prime modulus.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Junsoo Ha,