2001/04/30 by Pieter Moree
Mathematics · #math.NT #msc:11R45 #msc:11B37
published as Japan J. Math. 29 (2003), 143-157 · 13 pages
arxiv created 2003/10/13 · arxiv updated 2009/11/30
Let g be a non-zero rational number. Let Ng,t(x) denote the number of primes p<=x for which the subgroup of the multiplicative group of the finite field having p elements that is generated by g mod p is of residual index t. In Part I, which is published in J. Number Theory 83 (2000), 155-181, a heuristic for Ng,t(x) was set up, under the assumption of the Generalized Riemann Hypothesis (GRH), and shown to be asymptotically exact. In this preprint we provide an alternative and rather shorter proof of this result.