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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.
Keywords: Log-Sine Integrals; Mahler Measure; Multiple Polylogarithms; Multiple Zeta Values; Clausen Functions
Received: 2011-05-15
Accepted: 2011-11-26
Published Online: 2012-11-30
Published in Print: 2012-12-01
© 2012 by Walter de Gruyter Berlin Boston
