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Integers


Mathematical Citation Quotient (MCQ) 2015: 0.31

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1867-0660
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Log-Sine Evaluations of Mahler Measures, II

1Department of Mathematics, University of Western Ontario, London, Ontario, Canada

2Centre for Computer-assisted Research Mathematics and its Applications (CARMA), University of Newcastle, Callaghan, Australia

3Department of Mathematics, Tulane University, New Orleans, Louisiana, USA

4Centre for Computer-assisted Research Mathematics and its Applications (CARMA), University of Newcastle, Callaghan, Australia

Citation Information: Integers. Volume 12, Issue 6, Pages 1179–1212, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: 10.1515/integers-2012-0035, November 2012

Publication History

Received:
2011-05-15
Accepted:
2011-11-26
Published Online:
2012-11-30

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

Citing Articles

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[1]
Yoshitaka Sasaki
International Journal of Number Theory, 2015, Page 1
[2]
David H. Bailey, Jonathan M. Borwein, and Alexander D. Kaiser
Journal of Symbolic Computation, 2014, Volume 60, Page 120

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