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Mahler measure under variations of the base group
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Oliver T. Dasbach
Published/Copyright:
June 15, 2009
Abstract
We study properties of a generalization of the Mahler measure to elements in group rings, in terms of the Lück-Fuglede-Kadison determinant. Our main focus is the variation of the Mahler measure when the base group is changed. In particular, we study how to obtain the Mahler measure over an infinite group as limit of Mahler measures over finite groups, for example, in the classical case of the free abelian group or the infinite dihedral group, and others.
Received: 2008-01-02
Published Online: 2009-06-15
Published in Print: 2009-July
© de Gruyter 2009
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Articles in the same Issue
- The Noether Map I
- A general notion of algebraic entropy and the rank-entropy
- Computing the maximal algebra of quotients of a Lie algebra
- Mahler measure under variations of the base group
- Extremal α-pseudocompact abelian groups
- Group algebras whose symmetric and skew elements are Lie solvable
- Walks on graphs and lattices – effective bounds and applications
- Strichartz and smoothing estimates for Schrödinger operators with almost critical magnetic potentials in three and higher dimensions
- On the homotopy type of the non-completed classifying space of a p-local finite group
