On Primitive Roots of One-Dimensional Tori, Original Research Article

We exploit an analogue of Artinʹs primitive roots conjecture for one-dimensional tori over image. Let image be a one-dimensional torus over image, and let Pset membership, variantimage(image) 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 image(imageℓ).