Mahler measures and Fuglede-Kadison determinants

The Mahler measure of a function on the real d-torus is its geometric mean over the torus. It appears in number theory, ergodic theory and other fields. The Fuglede–Kadison determinant is defined in the context of von Neumann algebra theory and can be seen as a noncommutative generalization of the M...

Author: Deninger, Christopher
Division/Institute:FB 10: Mathematik und Informatik
Document types:Article
Media types:Text
Publication date:2009
Date of publication on miami:20.08.2009
Modification date:17.04.2015
Source:Münster Journal of Mathematics, 2 (2009), S. 45-64
Edition statement:[Electronic ed.]
DDC Subject:510: Mathematik
License:InC 1.0
Language:English
Format:PDF document
URN:urn:nbn:de:hbz:6-10569517585
Permalink:http://nbn-resolving.de/urn:nbn:de:hbz:6-10569517585
Digital documents:mjm_vol_2_04.pdf

The Mahler measure of a function on the real d-torus is its geometric mean over the torus. It appears in number theory, ergodic theory and other fields. The Fuglede–Kadison determinant is defined in the context of von Neumann algebra theory and can be seen as a noncommutative generalization of the Mahler measure. In the paper we discuss and compare theorems in both fields, especially approximation theorems by finite dimensional determinants. We also explain how to view Fuglede–Kadison determinants as continuous functions on the space of marked groups.