994 research outputs found

    Tame kernels and further 4-rank densites

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    There has been recent progress on computing the 4-rank of the tame kernel K2(OF)K_2(\mathcal{O}_F) for FF a quadratic number field. For certain quadratic number fields, this progress has led to "density results'' concerning the 4-rank of tame kernels. These results were first mentioned in \cite{CH} and proven in \cite{RO}. In this paper, we consider some additional quadratic number fields and obtain further density results of 4-ranks of tame kernels. Additionally, we give tables which might indicate densities in some generality.Comment: 20 page

    A note on 4-rank densities

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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.Comment: 9 page

    Densities of 4-ranks of K2(O)K_2(\mathcal{O})

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    Conner and Hurrelbrink established a method of determining the structure of the 2-Sylow subgroup of the tame kernel K2(O)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.Comment: 11 page
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