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

P. E. Conner, J. Hurrelbrink (1995)

Acta Arithmetica

A large number of papers have contributed to determining the structure of the tame kernel K 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 K 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,...

On the 2-primary part of K₂ of rings of integers in certain quadratic number fields

A. Vazzana (1997)

Acta Arithmetica

1. Introduction. For quadratic fields whose discriminant has few prime divisors, there are explicit formulas for the 4-rank of K E . For quadratic fields whose discriminant has arbitrarily many prime divisors, the formulas are less explicit. In this paper we will study fields of the form ( ( p . . . p k ) ) , where the primes p i are all congruent to 1 mod 8. We will prove a theorem conjectured by Conner and Hurrelbrink which examines under what conditions the 4-rank of K E is zero for such fields. In the course of proving...

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