Eisenstein cocycles on GL(n) and values of L-functions in imaginary quadratic extensions

Dedekind sums first appeared in the Dedekind's study of the functional equation for the Dedekind eta function.
R. Sczech showed that these sums in fact satisfy a cocycle property on GL(2), and generalized this relation,
defining Eisenstein cocycles on GL(n) over totally real fields. Using this construction, Sczech parametrized
values of certain zeta functions and gave a different proof of the Klingen-Siegel theorem on the rationality
of these values. In this talk, we report on generalizing Eisenstein cocycle for GL(n) toto extensions of an
imaginary quadratic fields. Using this, we parametrize values of certain Hecke L-functions considered by
P. Colmez, which were previously known to be algebraic. This is joint work with Florez and Karabulut.