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  • Titel
    Mahler measures and Fuglede-Kadison determinants
  • Verfasser
    Deninger, Christopher
  • Enthalten in
    Münster Journal of Mathematics, H. Münster Journal of Mathematics, S. 45-64
  • Erschienen
    2009
  • Sprache
    Englisch
  • Dokumenttyp
    Aufsatz in einer Zeitschrift
  • URN
    urn:nbn:de:hbz:6-10569517585 
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Abstract
  • 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.
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