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A Note on 4-Rank Densities

Published online by Cambridge University Press:  20 November 2018

Robert Osburn
Robert Osburn*
Affiliation:
Department of Mathematics Jeffery Hall Queen’s University Kingston, ON K7L 3N6, e-mail: [email protected]
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Abstract

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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.

Keywords

11R7019F9911R1111R45
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 3 , 01 September 2004 , pp. 431 - 438
Copyright
Copyright © Canadian Mathematical Society 2004

References

[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] Conner, P. E. and Hurrelbrink, J., On the 4-rank of the tame kernel K2(O) in positive definite terms. J. Number Theory 88 (2001), 263–282.Google Scholar
[3] Gerth, F., The 4-class ranks of quadratic fields. Invent.Math. 77 (1984), 489–515.Google Scholar
[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] Hurrelbrink, J., Circulant Graphs and 4-Ranks of Ideal Class Groups. Canad. J. Math. 46 (1994), 169–183.Google Scholar
[6] Osburn, R., Densities of 4-ranks of K2(O). Acta Arith. 102 (2002), 45–54.Google Scholar
[7] Murray, B. and Osburn, R., Tame kernels and further 4-rank densities. J. Number Theory, 98 (2003), 390–406.Google Scholar
[8] Qin, H., The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields. Acta Arith. 69 (1995), 153–169.Google Scholar
[9] Qin, H., The 4-ranks of K2(OF) for real quadratic fields. Acta Arith. 72 (1995), 323–333.Google Scholar
[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] Sanford, C., A product formula for detecting 4-torsion in K2 of quadratic number rings. M.S. thesis, McMaster University, 1999.Google Scholar