Log-sine evaluations of Mahler measures, II
Classical Analysis and ODEs
2011-03-17 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1103.3035,
title = {Log-sine evaluations of Mahler measures, II},
author = {David Borwein and Jonathan M. Borwein and Armin Straub and James Wan},
journal= {arXiv preprint arXiv:1103.3035},
year = {2011}
}
Comments
35 pages