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LOG-SINE EVALUATIONS OF MAHLER MEASURES

Published online by Cambridge University Press:  15 June 2012

JONATHAN M. BORWEIN
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia (email: jonathan.borwein@newcastle.edu.au)
ARMIN STRAUB*
Affiliation:
Department of Mathematics, Tulane University, New Orleans, LA 70118, USA (email: astraub@tulane.edu)
*
For correspondence; e-mail: astraub@tulane.edu
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Abstract

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We provide evaluations of several recently studied higher and multiple Mahler measures using log-sine integrals. This is complemented with an analysis of generating functions and identities for log-sine integrals which allows the evaluations to be expressed in terms of zeta values or more general polylogarithmic terms. The machinery developed is then applied to evaluation of further families of multiple Mahler measures.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

Footnotes

Borwein was supported in part by the Australian Research Council and the University of Newcastle.

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