On elementary abelian 2-Sylow K₂ of rings of integers of certain quadratic number fields

P. E. Conner, and J. Hurrelbrink. "On elementary abelian 2-Sylow K₂ of rings of integers of certain quadratic number fields." Acta Arithmetica 73.1 (1995): 59-65. <http://eudml.org/doc/206810>.

@article{P1995,
abstract = {A large number of papers have contributed to determining the structure of the tame kernel $K₂_F$ of algebraic number fields F. Recently, for quadratic number fields F whose discriminants have at most three odd prime divisors, 4-rank formulas for $K₂_F$ 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 $K₂_F$ is zero, computationally even more accessible. For arbitrary algebraic number fields F with 4-rank of $K₂_F$ 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.},
author = {P. E. Conner, J. Hurrelbrink},
journal = {Acta Arithmetica},
keywords = {quadratic number fields; positive definite binary quadratic forms; 2-Sylow subgroup; elementary abelian},
language = {eng},
number = {1},
pages = {59-65},
title = {On elementary abelian 2-Sylow K₂ of rings of integers of certain quadratic number fields},
url = {http://eudml.org/doc/206810},
volume = {73},
year = {1995},
}

TY - JOUR
AU - P. E. Conner
AU - J. Hurrelbrink
TI - On elementary abelian 2-Sylow K₂ of rings of integers of certain quadratic number fields
JO - Acta Arithmetica
PY - 1995
VL - 73
IS - 1
SP - 59
EP - 65
AB - A large number of papers have contributed to determining the structure of the tame kernel $K₂_F$ of algebraic number fields F. Recently, for quadratic number fields F whose discriminants have at most three odd prime divisors, 4-rank formulas for $K₂_F$ 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 $K₂_F$ is zero, computationally even more accessible. For arbitrary algebraic number fields F with 4-rank of $K₂_F$ 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.
LA - eng
KW - quadratic number fields; positive definite binary quadratic forms; 2-Sylow subgroup; elementary abelian
UR - http://eudml.org/doc/206810
ER -