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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Mahler measure and the WZ algorithm
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by Jesús Guillera and Mathew Rogers PDF
Proc. Amer. Math. Soc. 143 (2015), 2873-2886 Request permission

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”.
References
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Additional Information
  • Jesús Guillera
  • Affiliation: Av. Cesáreo Alierta, 31 esc. izda 4$^\circ$–A, Zaragoza, Spain
  • Email: jguillera@gmail.com
  • Mathew Rogers
  • Affiliation: Department of Mathematics, Université de Montréal, Montreal, Quebec, Canada
  • MR Author ID: 757548
  • ORCID: 0000-0001-9163-4890
  • Email: mathewrogers@gmail.com
  • 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
  • © Copyright 2015 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 3336612