A large number of papers have contributed to determining the structure of the tame kernel of algebraic number fields F. Recently, for quadratic number fields F whose discriminants have at most three odd prime divisors, 4-rank formulas for have been made very explicit by Qin Hourong in terms of the indefinite quadratic form x² - 2y² (see [7], [8]). We have made a successful effort, for quadratic number fields F = ℚ (√(±p₁p₂)), to characterize in terms of positive definite binary quadratic forms, when the 2-Sylow subgroup of the tame kernel of F is elementary abelian. This makes determining exactly when the 4-rank of is zero, computationally even more accessible. For arbitrary algebraic number fields F with 4-rank of equal to zero, it has been pointed out that the Leopoldt conjecture for the prime 2 is valid for F, compare [6]. We consider this paper to be an addendum to the Acta Arithmetica publications [7], [8]. It grew out of our circulated 1989 notes [3]. Acknowledgements. We gratefully acknowledge fruitful long-term communications on this topic with Jerzy Browkin.
@article{bwmeta1.element.bwnjournal-article-aav73i1p59bwm,
author = {P. E. Conner and J. Hurrelbrink},
title = {On elementary abelian 2-Sylow K2 of rings of integers of certain quadratic number fields},
journal = {Acta Arithmetica},
volume = {69},
year = {1995},
pages = {59-65},
zbl = {0844.11072},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav73i1p59bwm}
}
P. E. Conner; J. Hurrelbrink. On elementary abelian 2-Sylow K₂ of rings of integers of certain quadratic number fields. Acta Arithmetica, Tome 69 (1995) pp. 59-65. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav73i1p59bwm/
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