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Mahler measure and the WZ algorithm


Authors: Jesús Guillera and Mathew Rogers
Journal: Proc. Amer. Math. Soc. 143 (2015), 2873-2886
MSC (2010): Primary 33C20, 33F10; Secondary 19F27
DOI: https://doi.org/10.1090/S0002-9939-2015-12240-X
Published electronically: March 18, 2015
MathSciNet review: 3336612
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Abstract: We use the Wilf-Zeilberger method to prove identities between Mahler measures of polynomials. In particular, we offer a new proof of a formula due to Lalín, and we show how to translate the identity into a formula involving elliptic dilogarithms. This work settles a challenge problem proposed by Kontsevich and Zagier in their paper, ``Periods''.


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Additional Information

Jesús Guillera
Affiliation: Av. Cesáreo Alierta, 31 esc. izda 4$^{∘}$–A, Zaragoza, Spain
Email: jguillera@gmail.com

Mathew Rogers
Affiliation: Department of Mathematics, Université de Montréal, Montreal, Quebec, Canada
Email: mathewrogers@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2015-12240-X
Received by editor(s): March 6, 2013
Received by editor(s) in revised form: March 29, 2013
Published electronically: March 18, 2015
Additional Notes: The second author was supported by the National Science Foundation award DMS-0803107.
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.