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LOG-SINE EVALUATIONS OF MAHLER MEASURES

Part of: Other special functions Algebraic number theory: global fields

Published online by Cambridge University Press:  15 June 2012

JONATHAN M. BORWEIN  and
ARMIN STRAUB
JONATHAN M. BORWEIN
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia (email: [email protected])
ARMIN STRAUB*
Affiliation:
Department of Mathematics, Tulane University, New Orleans, LA 70118, USA (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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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.

Keywords

log-sine integralsMahler measuremultiple polylogarithmsmultiple zeta valuesClausen functions

MSC classification

Secondary: 33E20: Other functions defined by series and integrals 11R06: PV-numbers and generalizations; other special algebraic numbers; Mahler measure
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 92 , Issue 1 , February 2012 , pp. 15 - 36
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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