Name: An algebraic integration for Mahler measure
Creator: Lalín, Matilde N.
Keywords: Mathematics - Number Theory, 11G55, K-Theory and Homology (math.KT), $K$-theory in number theory, 01 natural sciences, 19F99, Dirichlet $L$-series, regulator, Mahler measure, Mathematics - K-Theory and Homology

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 15 Jun 2007Embargo end date: 01 Jan 2006Publisher:Duke University PressJournal:Duke Mathematical Journal, volume 138 (issn: 0012-7094,

Authors: Lalín, Matilde N.;

doi: 10.1215/s0012-7094-07-13832-8 , 10.48550/arxiv.math/0609851

arXiv: math/0609851

An algebraic integration for Mahler measure

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Abstract

There are many examples of several-variable polynomials whose Mahler measure is expressed in terms of special values of polylogarithms. These examples are expected to be related to computations of regulators, as observed by Deninger, and later Rodriguez-Villegas, and Maillot. While Rodriguez-Villegas made this relationship explicit for the two variable case, it is our goal to understand the three variable case and shed some light on the examples with more variables.

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University of British Columbia
Canada

Keywords

Mathematics - Number Theory, 11G55, K-Theory and Homology (math.KT), $K$-theory in number theory, 19F99, Dirichlet $L$-series, regulator, Mahler measure, Mathematics - K-Theory and Homology, differential form, FOS: Mathematics, 11G55, 19F99, Number Theory (math.NT), polylogarithms, Polylogarithms and relations with $K$-theory

6 Research products, page 1 of 1

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