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Functional equations for Mahler measures of genus-one curves
by
Matilde N. Lalin
UBC-PIMS, MPIfM, University of Alberta
Coauthors: Mathew Rogers (UBC)
The Mahler measure of an n-variable polynomial P is the integral of log - P - over the n-dimensional unit torus Tn with the Haar measure. For one-variable polynomials, this is a natural quantity that appears in different problems such as Lehmer's question. For the several-variable case many examples are known for which the Mahler measure is related to special values of L-functions. Consider a family of polynomials whose coefficients depend on one parameter. Then the Mahler measure is a function of that parameter. There are examples for which this function satisfies functional equations that may be deduced from modularity properties or evaluations of elliptic regulators following works by Rodriguez-Villegas, Deninger, and others. These equations may allow us to prove new identities of Mahler measures.
Date received: May 24, 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 # cavb-18.