### Deligne periods of mixed motives, K-theory and the entropy of certain Z^n-actions, by Christopher Deninger

In this paper we relate Mahler measures of polynomials over Q in favourable
instances to the regulator of symbols in algebraic K-theory and to Deligne
periods of mixed motives. By the known relation of Mahler measures with entropies of dynamical systems of algebraic origin we therefore obtain in
many instances a relation of symbols and periods with entropies.
In one example using the Beilinson conjectures we find a conjectural expression
of a certain Mahler measure or entropy in terms of the L-series of an elliptic
curve at s=2.

Christopher Deninger <deninge@math.uni-muenster.de>