A quadratic analogue of Artin's conjecture on primitive roots.
Let \(\epsilon\) be a fundamental unit in a real quadratic field \(k\), and let \(S\) be the set of rational primes \(p\) for which \(\varepsilon\) has maximal order modulo \(p\). Under the assumption of the generalized Riemann hypothesis, we show that \(S\) has a density \(\delta (S)=c\cdot A\) in the set of all rational primes, where \(A\) is Artin's constant and \(c\) is a positive rational number. In the proof the author uses techniques of \textit{C. Hooley} [J. Reine Angew. Math. 225, 209--220 (1967; Zbl 0221.10048)] and results of the splitting behaviour of primes in subfields of the Kummer extension \(\mathbb Q(\zeta_l,{\root l\of\varepsilon})\). In the Erratum the statements of Lemma 6, Lemma 7c, Theorem 2a, and Theorem 2b are corrected.
scientific article; zbMATH DE number 1420265