Fix an element in a quadratic field . Define as the set of rational primes , for which has maximal order modulo . Under the assumption of the generalized Riemann hypothesis, we show that has a density. Moreover, we give necessary and sufficient conditions for the density of to be positive.
Soit fixé dans un corps quadratrique . On note l’ensemble des nombres premiers pour lesquels admet un ordre maximal modulo . Sous G.R.H., on montre que a une densité. Nous donnons aussi des conditions nécessaires et suffisantes pour que cette densité soit strictement positive.
@article{JTNB_2002__14_1_287_0, author = {Hans Roskam}, title = {Artin's primitive root conjecture for quadratic fields}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {287--324}, publisher = {Universit\'e Bordeaux I}, volume = {14}, number = {1}, year = {2002}, zbl = {1026.11086}, mrnumber = {1926004}, language = {en}, url = {https://jtnb.centre-mersenne.org/item/JTNB_2002__14_1_287_0/} }
TY - JOUR AU - Hans Roskam TI - Artin's primitive root conjecture for quadratic fields JO - Journal de théorie des nombres de Bordeaux PY - 2002 SP - 287 EP - 324 VL - 14 IS - 1 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/item/JTNB_2002__14_1_287_0/ LA - en ID - JTNB_2002__14_1_287_0 ER -
Hans Roskam. Artin's primitive root conjecture for quadratic fields. Journal de théorie des nombres de Bordeaux, Volume 14 (2002) no. 1, pp. 287-324. https://jtnb.centre-mersenne.org/item/JTNB_2002__14_1_287_0/
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