Log-sine evaluations of Mahler measures, II
David Borwein, Jonathan M. Borwein, Armin Straub, James Wan
TL;DR
This paper advances the evaluation of Mahler measures using log-sine integrals, providing new reduction techniques, detailed studies of multiple polylogarithms, and proofs of conjectures by Boyd.
Contribution
It introduces methods to reduce multiple Mahler measures and offers proofs for two of Boyd's conjectures using log-sine integrals.
Findings
Reduced several multiple Mahler measures
Provided detailed analysis of multiple polylogarithms
Supplied proofs for two Boyd conjectures
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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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Advanced Combinatorial Mathematics