On the 𝑟-rank Artin Conjecture

Author:

Pappalardi Francesco

Abstract

We assume the generalized Riemann hypothesis and prove an asymptotic formula for the number of primes for which F p \mathbb {F}_p^* can be generated by r r given multiplicatively independent numbers. In the case when the r 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 10 4 9\cdot 10^4 .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

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