A generalisation of Mahler measure and its application in algebraic dynamical systems
Volume 88 / 1999
Acta Arithmetica 88 (1999), 15-29
DOI: 10.4064/aa-88-1-15-29
Abstract
We prove a generalisation of the entropy formula for certain algebraic $ℤ^d$-actions given in [2] and [4]. This formula expresses the entropy as the logarithm of the Mahler measure of a Laurent polynomial in d variables with integral coefficients. We replace the rational integers by the integers in a number field and examine the entropy of the corresponding dynamical system.
