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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Borwein, Jonathan M. Straub, Armin and Vignat, Christophe 2016. Densities of short uniform random walks in higher dimensions. Journal of Mathematical Analysis and Applications, Vol. 437, Issue. 1, p. 668.


    Pardo, Luis M. and Pardo, Mario 2016. On the zeta Mahler measure function of the Jacobian determinant, condition numbers and the height of the generic discriminant. Applicable Algebra in Engineering, Communication and Computing, Vol. 27, Issue. 4, p. 303.


    Borwein, Jonathan M. and Straub, Armin 2013. Mahler measures, short walks and log-sine integrals. Theoretical Computer Science, Vol. 479, p. 4.


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  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society, Volume 92, Issue 1
  • February 2012, pp. 15-36

LOG-SINE EVALUATIONS OF MAHLER MEASURES

  • JONATHAN M. BORWEIN (a1) and ARMIN STRAUB (a2)
  • DOI: http://dx.doi.org/10.1017/S1446788712000067
  • Published online: 15 June 2012
Abstract
Abstract

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.

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Corresponding author
For correspondence; e-mail: astraub@tulane.edu
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Borwein was supported in part by the Australian Research Council and the University of Newcastle.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

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[16]N. Kurokawa , M. Lalín and H. Ochiai , ‘Higher Mahler measures and zeta functions’, Acta Arith. 135(3) (2008), 269297.

[17]M. Lalín and K. Sinha , ‘Higher Mahler measure of cyclotomic polynomials and Lehmer’s question’, Ramanujan J. 26 (2011), 257294.

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[22]Y. Sasaki , ‘On multiple higher Mahler measures and multiple L values’, Acta Arith. 144(2) (2010), 159165.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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