Asymptotically exact heuristics for (near) primitive roots. II

Details Asymptotically exact heuristics for (near) primitive roots. II Asymptotically exact heuristics for (near) primitive roots. II

2001-04-13

arxiv.org/abs/math/0104148v2

Japan J. Math. 29 (2003), 143-157

Mathematics

Number Theory

13 pages

Scientific paper

Let g be a non-zero rational number. Let N_{g,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 N_{g,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.

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