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Integers


Mathematical Citation Quotient (MCQ) 2016: 0.40

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

David Borwein / Jonathan M. Borwein
  • Centre for Computer-assisted Research Mathematics and its Applications (CARMA), University of Newcastle, Callaghan, Australia
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/ Armin Straub / James Wan
  • Centre for Computer-assisted Research Mathematics and its Applications (CARMA), University of Newcastle, Callaghan, Australia
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Published Online: 2012-11-30 | DOI: https://doi.org/10.1515/integers-2012-0035

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

About the article

Received: 2011-05-15

Accepted: 2011-11-26

Published Online: 2012-11-30

Published in Print: 2012-12-01


Citation Information: Integers, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integers-2012-0035.

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© 2012 by Walter de Gruyter Berlin Boston. Copyright Clearance Center

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Yoshitaka Sasaki
International Journal of Number Theory, 2015, Volume 11, Number 07, Page 2239
[2]
David H. Bailey, Jonathan M. Borwein, and Alexander D. Kaiser
Journal of Symbolic Computation, 2014, Volume 60, Page 120

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