Artin's primitive root conjecture for quadratic fields
Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 1, pp. 287-324

Fix an element α in a quadratic field K. Define S as the set of rational primes p, for which α 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.

Soit α fixé dans un corps quadratrique K. On note S l’ensemble des nombres premiers p pour lesquels α admet un ordre maximal modulo p. Sous G.R.H., on montre que S a une densité. Nous donnons aussi des conditions nécessaires et suffisantes pour que cette densité soit strictement positive.

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     title = {Artin's primitive root conjecture for quadratic fields},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {287--324},
     year = {2002},
     publisher = {Universit\'e Bordeaux I},
     volume = {14},
     number = {1},
     zbl = {1026.11086},
     mrnumber = {1926004},
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     url = {https://jtnb.centre-mersenne.org/item/JTNB_2002__14_1_287_0/}
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Hans Roskam. Artin's primitive root conjecture for quadratic fields. Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 1, pp. 287-324. https://jtnb.centre-mersenne.org/item/JTNB_2002__14_1_287_0/

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