Roskam: Artin's primitive root conjecture for quadratic fields

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Hans Roskam
Artin's primitive root conjecture for quadratic fields
Journal de théorie des nombres de Bordeaux, 14 no. 1 (2002), p. 287-324, doi: 10.5802/jtnb.360
Article PDF | Reviews MR 1926004 | Zbl 1026.11086 | 1 citation in Cedram

Résumé - Abstract

Fix an element $\alpha $ in a quadratic field $K$. Define $S$ as the set of rational primes $p$, for which $\alpha $ has maximal order modulo $p$. Under the assumption of the generalized Riemann hypothesis, we show that $S$ has a density. Moreover, we give necessary and sufficient conditions for the density of $S$ to be positive.

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