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Mathematics of Computation

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On the $r$-rank Artin Conjecture

Author: Francesco Pappalardi
Journal: Math. Comp. 66 (1997), 853-868
MSC (1991): Primary 11N37; Secondary 11N56
MathSciNet review: 1377664
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Abstract: We assume the generalized Riemann hypothesis and prove an asymptotic formula for the number of primes for which $\mathbb{F}^\ast_p$ can be generated by $r$ given multiplicatively independent numbers. In the case when the $r$ 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 $9\cdot 10^4$.

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Francesco Pappalardi
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