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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 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.

Titel: Mahler measures and Fuglede-Kadison determinants
Verfasser: Deninger, Christopher GND
Organisation: FB 10: Mathematik und Informatik
Dokumenttyp: Artikel
Medientyp: Text
Erscheinungsdatum: 2009
Publikation in MIAMI: 20.08.2009
Datum der letzten Änderung: 17.04.2015
Zeitschrift/Periodikum: Münster Journal of Mathematics / 2 (2009), S. 45 - 64
Fachgebiete: Mathematik
Sprache: Englisch
Format: PDF-Dokument
URN: urn:nbn:de:hbz:6-10569517585