Densities of 4-ranks of $K_2(\mathcal{O})$

Details Densities of 4-ranks of $K_2(\mathcal{O})$ Densities of 4-ranks of $K_2(\mathcal{O})$

2007-03-12

arxiv.org/abs/math/0703322v1

Acta Arith. 102 (2002), no. 1, 45-54

Mathematics

Number Theory

11 pages

Scientific paper

Conner and Hurrelbrink established a method of determining the structure of the 2-Sylow subgroup of the tame kernel $K_2(\mathcal{O})$ for certain quadratic number fields. Specifically, the 4-rank for these fields was characterized in terms of positive definite binary quadratic forms. Numerical calculations led to questions concerning possible density results of the 4-rank of tame kernels. In this paper, we succeed in giving affirmative answers to these questions.

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