Signed fundamental domains for number fields

The usual embedding of a number field K into a Euclidean space V gives rise to an action of
the units of K on V.  Good fundamental domains for this action are important in the study of
abelian L-functions. However, they are usually hard to come by. In this talk, we will describe
a method to deform easy but useless fundamental domains into signed versions of good ones.
This is a joint work with Eduardo Friedman.