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Log-Sine Evaluations of Mahler Measures, II
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David Borwein
,
Jonathan M. Borwein
Published/Copyright:
November 30, 2012
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
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- Preface to the John Selfridge Memorial Issue
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- On a Conjecture Regarding Balancing with Powers of Fibonacci Numbers
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Keywords for this article
Log-Sine Integrals;
Mahler Measure;
Multiple Polylogarithms;
Multiple Zeta Values;
Clausen Functions
Articles in the same Issue
- Masthead
- Preface to the John Selfridge Memorial Issue
- Numbers with Integer Complexity Close to the Lower Bound
- On a Conjecture Regarding Balancing with Powers of Fibonacci Numbers
- Perfect Powers with Few Ternary Digits
- On Mullin's Second Sequence of Primes
- Log-Sine Evaluations of Mahler Measures, II
- On Odd Perfect Numbers and Even 3-Perfect Numbers
- Euler Pseudoprimes for Half of the Bases
- Odd Incongruent Restricted Disjoint Covering Systems
- Cubes in {0,1,...,n}3
- Sierpiński Numbers in Imaginary Quadratic Fields
- On a Partition Problem of Canfield and Wilf
- The 392 Problem
- Artin's Primitive Root Conjecture – A Survey
- Prime-Perfect Numbers
- Explicit Solutions of Certain Systems of Pell Equations
- The Search for Aurifeuillian-Like Factorizations
- Some Monoapparitic Fourth Order Linear Divisibility Sequences
- A Note from the Editors
