An algebraic integration for Mahler measure

Details An algebraic integration for Mahler measure An algebraic integration for Mahler measure

2006-09-29

arxiv.org/abs/math/0609851v1

Duke Math. J. 138 (2007), no. 3, 391--422

Mathematics

Number Theory

3 figures

Scientific paper

10.1215/S0012-7094-07-13832-8

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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