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# A Note on $4$-Rank Densities

Published:2004-09-01
Printed: Sep 2004
• Robert Osburn
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## Abstract

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.
 MSC Classifications: 11R70 - $K$-theory of global fields [See also 19Fxx] 19F99 - None of the above, but in this section 11R11 - Quadratic extensions 11R45 - Density theorems