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 <>