Log-sine evaluations of Mahler measures, II

This article by David Borwein, Jonathan M. Borwein, Armin Straub and James Wan has been published in Integers (Selfridge memorial volume) (to appear).

You can also find this article on the arXiv as 1103.3035v1 [math.CA].

Abstract

We continue the analysis of higher and multiple Mahler measures using log-sine integrals as started in "Log-sine evaluations of Mahler measures" and "Special values of generalized log-sine integrals" by two of the authors. This motivates a detailed study of various multiple polylogarithms and worked examples are given. Our techniques enable the reduction of several multiple Mahler measures, and supply an easy proof of two conjectures by Boyd.

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