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}, doi = {10.5802/jtnb.360}, zbl = {1026.11086}, mrnumber = {1926004}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.360/} }
TY - JOUR TI - Artin's primitive root conjecture for quadratic fields JO - Journal de Théorie des Nombres de Bordeaux PY - 2002 DA - 2002/// SP - 287 EP - 324 VL - 14 IS - 1 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.360/ UR - https://zbmath.org/?q=an%3A1026.11086 UR - https://www.ams.org/mathscinet-getitem?mr=1926004 UR - https://doi.org/10.5802/jtnb.360 DO - 10.5802/jtnb.360 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. doi : 10.5802/jtnb.360. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.360/
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