We exploit an analogue of Artin's primitive roots conjecture for one-dimensional tori over ℚ. Let T be a one-dimensional torus over ℚ, and let P ε T(ℚ) be a nontorsion point. Under Generalized Riemann Hypothesis, we derive an explicit density formula for the set of rational primes ℓ such that P modulo ℓ generates T(Fℓ).
- Primitive roots
- Quadratic fields