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Higher Mahler measure of an $n$-variable family

Volume 174 / 2016

Matilde N. Lalín, Jean-Sébastien Lechasseur Acta Arithmetica 174 (2016), 1-30 MSC: Primary 11R06; Secondary 11M06, 11R09. DOI: 10.4064/aa8111-3-2016 Published online: 13 June 2016

Abstract

We prove formulas for the $k$-higher Mahler measure of a family of rational functions with an arbitrary number of variables. Our formulas reveal relations with multiple polylogarithms evaluated at certain roots of unity.

Authors

  • Matilde N. LalínDépartement de Mathématiques et de Statistique
    Université de Montréal
    CP 6128, succ. Centre-ville
    Montreal, QC H3C 3J7, Canada
    e-mail
  • Jean-Sébastien LechasseurDépartement de Mathématiques et de Statistique
    Université de Montréal
    CP 6128, succ. Centre-ville
    Montreal, QC H3C 3J7, Canada
    e-mail

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