On primes p for which d divides ord_p(g)
Number Theory
2016-09-07 v1
Abstract
Let N_g(d) be the set of primes p such that the order of g modulo p is divisible by a prescribed integer d. Wiertelak showed that this set has a natural density and gave a rather involved explicit expression for it. Let N_g(d)(x) be the number of primes p<=x that are in N_g(d). A simple identity for N_g(d)(x) is established. It is used to derive a more compact expression for the natural density than known hitherto. A numerical demonstration, using a program of Y. Gallot, is presented.
Cite
@article{arxiv.math/0407421,
title = {On primes p for which d divides ord_p(g)},
author = {Pieter Moree},
journal= {arXiv preprint arXiv:math/0407421},
year = {2016}
}
Comments
10 pages, 3 tables