Log-sine evaluations of Mahler measures, II

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.

35 pages

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Cited by in corpus (3)

• The Epsilon Expansion of Feynman Diagrams via Hypergeometric Functions and Differential Reduction
• Special Values of Generalized Log-sine Integrals
• Log-sine evaluations of Mahler measures