### Algebraic K-theory and twisted reciprocity laws, by Bruno Kahn

We extend the classical reciprocity laws of algebraic number theory to
higher odd K-groups of algebraic integers. Moreover, we show that a
suitable renormalisation of the corresponding ``twisted Legendre symbols"
is independent ``in the average" from the chosen prime when the
number field considered is Galois over Q. This seems new even in the
classical case.

Bruno Kahn <kahn@math.jussieu.fr>