Atlas home || Conferences | Abstracts | about Atlas

A second time around the Volume Conjecture
May 30 - June 3, 2007
Louisiana State University
Baton Rouge, LA, USA

Organizers
Abhijit Champanerkar, Oliver Dasbach, Effie Kalfagianni, Ilya Kofman, Walter Neumann, Neal Stoltzfus

View Abstracts
Conference Homepage

Mahler measures under variations of the base group
by
Matilde N. Lalin
UBC-PIMS, Max-Planck-Institut fuer Mathematik, University of Alberta
Coauthors: Oliver T. Dasbach (Louisiana State University)

The Mahler measure of an n-variable polynomial P is the integral of log|P| over the n-dimensional unit torus T^n with the Haar measure. For one-variable polynomials, this is a natural quantity that appears in different problems such as Lehmer's question.

We consider a generalization of the Mahler measure to elements in group rings, in terms of the Lueck-Fuglede-Kadison determinant. We study the variation of the Mahler measure when the base group changes. In particular, we discuss the Mahler measure over infinite groups as limit of Mahler measures over finite groups.

Date received: May 23, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caus-14.