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Search: MSC category 11R70 ( $K$-theory of global fields [See also 19Fxx] )

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1. CMB 2015 (vol 58 pp. 620)

Sands, Jonathan W.
$L$-functions for Quadratic Characters and Annihilation of Motivic Cohomology Groups
Let $n$ be a positive even integer, and let $F$ be a totally real number field and $L$ be an abelian Galois extension which is totally real or CM. Fix a finite set $S$ of primes of $F$ containing the infinite primes and all those which ramify in $L$, and let $S_L$ denote the primes of $L$ lying above those in $S$. Then $\mathcal{O}_L^S$ denotes the ring of $S_L$-integers of $L$. Suppose that $\psi$ is a quadratic character of the Galois group of $L$ over $F$. Under the assumption of the motivic Lichtenbaum conjecture, we obtain a non-trivial annihilator of the motivic cohomology group $H_\mathcal{M}^2(\mathcal{O}_L^S,\mathbb{Z}(n))$ from the lead term of the Taylor series for the $S$-modified Artin $L$-function $L_{L/F}^S(s,\psi)$ at $s=1-n$.

Keywords:motivic cohomology, regulator, Artin L-functions
Categories:11R42, 11R70, 14F42, 19F27

2. CMB 2004 (vol 47 pp. 431)

Osburn, Robert
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.

Categories:11R70, 19F99, 11R11, 11R45

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