A Note on 4-Rank Densities
Canadian mathematical bulletin, Tome 47 (2004) no. 3, pp. 431-438

Voir la notice de l'article provenant de la source Cambridge University Press

For certain real quadratic number fields, we prove density results concerning 4-ranks of tame kernels. We also discuss a relationship between 4-ranks of tame kernels and 4-class ranks of narrow ideal class groups. Additionally, we give a product formula for a local Hilbert symbol.
DOI : 10.4153/CMB-2004-042-1
Mots-clés : 11R70, 19F99, 11R11, 11R45
Osburn, Robert. A Note on 4-Rank Densities. Canadian mathematical bulletin, Tome 47 (2004) no. 3, pp. 431-438. doi: 10.4153/CMB-2004-042-1
@article{10_4153_CMB_2004_042_1,
     author = {Osburn, Robert},
     title = {A {Note} on {4-Rank} {Densities}},
     journal = {Canadian mathematical bulletin},
     pages = {431--438},
     year = {2004},
     volume = {47},
     number = {3},
     doi = {10.4153/CMB-2004-042-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-042-1/}
}
TY  - JOUR
AU  - Osburn, Robert
TI  - A Note on 4-Rank Densities
JO  - Canadian mathematical bulletin
PY  - 2004
SP  - 431
EP  - 438
VL  - 47
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-042-1/
DO  - 10.4153/CMB-2004-042-1
ID  - 10_4153_CMB_2004_042_1
ER  - 
%0 Journal Article
%A Osburn, Robert
%T A Note on 4-Rank Densities
%J Canadian mathematical bulletin
%D 2004
%P 431-438
%V 47
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-042-1/
%R 10.4153/CMB-2004-042-1
%F 10_4153_CMB_2004_042_1

[1] [1] Batut, D., Bernardi, C., Cohen, H. and Olivier, M., GP-PARI, version 2.1.1, available at http://www.parigp-home.de/. Google Scholar

[2] [2] Conner, P. E. and Hurrelbrink, J., On the 4-rank of the tame kernel K(O) in positive definite terms. J. Number Theory 88 (2001), 263–282. Google Scholar

[3] [3] Gerth, F., The 4-class ranks of quadratic fields. Invent.Math. 77 (1984), 489–515. Google Scholar

[4] [4] Hurrelbrink, J. and Kolster, M., Tame kernels under relative quadratic extensions and Hilbert symbols. J. Reine Angew.Math. 499 (1998), 145–188. Google Scholar

[5] [5] Hurrelbrink, J., Circulant Graphs and 4-Ranks of Ideal Class Groups. Canad. J. Math. 46 (1994), 169–183. Google Scholar

[6] [6] Osburn, R., Densities of 4-ranks of K(O). Acta Arith. 102 (2002), 45–54. Google Scholar

[7] [7] Murray, B. and Osburn, R., Tame kernels and further 4-rank densities. J. Number Theory, 98 (2003), 390–406. Google Scholar

[8] [8] Qin, H., The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields. Acta Arith. 69 (1995), 153–169. Google Scholar

[9] [9] Qin, H., The 4-ranks of K(OF) for real quadratic fields. Acta Arith. 72 (1995), 323–333. Google Scholar

[10] [10] Rédei, L., Arithmetischer Beweis des Satzes über die Anzahl der durch 4 reilbaren Invarianten der absoluten Klassengruppe im quadratischen Zahlkörper. J. Reine Angew.Math. 171 (1934), 55–60. Google Scholar

[11] [11] Sanford, C., A product formula for detecting 4-torsion in K of quadratic number rings. M.S. thesis, McMaster University, 1999. Google Scholar

Cité par Sources :