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Log-sine evaluations of Mahler measures, II

Log-sine evaluations of Mahler measures, II
David Borwein, Jonathan M. Borwein, Armin Straub, James Wan — Integers — Selfridge memorial volume — Volume 12, Number 6, 2012, Pages 1179-1212

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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BibTeX

@article{logsin2-2012,
    author = {David Borwein and Jonathan M. Borwein and Armin Straub and James Wan},
    title = {Log-sine evaluations of {M}ahler measures, {II}},
    journal = {Integers},
    year = {2012},
    volume = {12},
    number = {6},
    pages = {1179--1212},
    doi = {10.1515/integers-2012-0035},
}