Indices in a Number Field
Mohamed Ayad; Rachid Bouchenna; Omar Kihel
Journal de Théorie des Nombres de Bordeaux, Volume 29 (2017) no. 1, p. 201-216

Let K be a number field, A be its ring of integers and p be a prime number. In this paper, we define a function μ K (p) which counts the number of θ ¯A/pA such that the index of θ is divisible by p. We give as well an explicit formula for it. Moreover, we show that the value of μ K (p) determines in some cases the splitting type of p in K.

Soient K un corps de nombres, A son anneau des entiers et p un nombre premier. Nous définissons une fonction μ K (p) qui compte le nombre de θ ¯A/pA d’indice multiple de p tout en en donnant une formule explicite. De plus, nous montrons que la valeur de μ K (p) détermine dans certains cas le type de décomposition de p dans K.

Received : 2015-03-12
Accepted : 2015-11-14
Published online : 2017-01-27
DOI : https://doi.org/10.5802/jtnb.976
Classification:  11R04,  12Y05
Keywords: Dedekind theorem, Common factor of indices.
@article{JTNB_2017__29_1_201_0,
     author = {Mohamed Ayad and Rachid Bouchenna and Omar Kihel},
     title = {Indices in a Number Field},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {29},
     number = {1},
     year = {2017},
     pages = {201-216},
     doi = {10.5802/jtnb.976},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_2017__29_1_201_0}
}
Ayad, Mohamed; Bouchenna, Rachid; Kihel, Omar. Indices in a Number Field. Journal de Théorie des Nombres de Bordeaux, Volume 29 (2017) no. 1, pp. 201-216. doi : 10.5802/jtnb.976. https://jtnb.centre-mersenne.org/item/JTNB_2017__29_1_201_0/

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