Abstract
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).
| Original language | English |
|---|---|
| Pages (from-to) | 23-33 |
| Number of pages | 11 |
| Journal | Journal of Number Theory |
| Volume | 93 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2002 |
Keywords
- Density
- Primitive roots
- Quadratic fields
- Torus