994 research outputs found
Tame kernels and further 4-rank densites
There has been recent progress on computing the 4-rank of the tame kernel
for 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
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
Conner and Hurrelbrink established a method of determining the structure of
the 2-Sylow subgroup of the tame kernel 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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