On the -rank Artin Conjecture
Abstract: We assume the generalized Riemann hypothesis and prove an asymptotic formula for the number of primes for which can be generated by given multiplicatively independent numbers. In the case when the given numbers are primes, we express the density as an Euler product and apply this to a conjecture of Brown-Zassenhaus (J. Number Theory 3 (1971), 306-309). Finally, in some examples, we compare the densities approximated with the natural densities calculated with primes up to .
Affiliation: Dipartimento di Matematica, Università degli Studi di Roma Tre, Via C. Segre, 2, 00146 Rome, Italy
Keywords: Primitive roots, generalized Riemann hypothesis
Received by editor(s): April 11, 1995
Received by editor(s) in revised form: January 23, 1996
Additional Notes: Supported by Human Capital and Mobility Program of the European Community, under contract ERBCHBICT930706
Article copyright: © Copyright 1997 American Mathematical Society