A Quadratic Analogue of Artinʹs Conjecture on Primitive Roots Original Research Article

Let var epsilon be a fundamental unit in a real quadratic field and let S be the set of rational primes p for which var epsilon has maximal order modulo p. Under the assumption of the generalized Riemann hypothesis, we show that S has a density δ(S)=c·A in the set of all rational primes, where A is Artinʹs constant and c is a positive rational number.