The Least Prime Primitive Root and the Shifted Sieve

Details The Least Prime Primitive Root and the Shifted Sieve The Least Prime Primitive Root and the Shifted Sieve

1998-07-20

arxiv.org/abs/math/9807104v1

Acta Arith. 80 (1997), no. 3, 277-288

Mathematics

Number Theory

10 pages

Scientific paper

We derive, for all prime moduli p except those in a very thin set, an upper bound for the least prime primitive root (mod p) of order of magnitude a constant power of log p. The improvement over previous results, where the upper bound was log p to an exponent tending to infinity with p, lies in the use of the linear sieve (a particular version called the shifted sieve) rather than Brun's sieve. The same methods allow us to rederive a conditional result of Shoup on the least prime primitive root (mod p) for all prime moduli p, assuming the generalized Riemann hypothesis. We also extend both results to composite moduli q, where the analogue of a primitive root is an element of maximal multiplicative order (mod q).

Affiliated with

Also associated with

No associations

Rating

The Least Prime Primitive Root and the Shifted Sieve does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Least Prime Primitive Root and the Shifted Sieve, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Least Prime Primitive Root and the Shifted Sieve will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-593030