Entanglement and Artin's primitive root conjecture

Artin's primitive root conjecture gives for a non-zero integer x an
expression for the density of prime numbers q for which x is a
primitive root modulo q. In this talk we consider generalizations
to number fields and rank one tori over number fields.
We show how the additive relations between certain radicals, as
captured in the ``entanglement group'', give a rational correction
factor to the straightforward generic answer.