Higher Mahler measure of an n-variable family

Matilde N. Lalín, and Jean-Sébastien Lechasseur. "Higher Mahler measure of an n-variable family." Acta Arithmetica 174.1 (2016): 1-30. <http://eudml.org/doc/286323>.

@article{MatildeN2016,
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.},
author = {Matilde N. Lalín, Jean-Sébastien Lechasseur},
journal = {Acta Arithmetica},
keywords = {Mahler measure; higher Mahler measure; special values of $\zeta $(s) and Dirichlet L-functions; polylogarithms},
language = {eng},
number = {1},
pages = {1-30},
title = {Higher Mahler measure of an n-variable family},
url = {http://eudml.org/doc/286323},
volume = {174},
year = {2016},
}

TY - JOUR
AU - Matilde N. Lalín
AU - Jean-Sébastien Lechasseur
TI - Higher Mahler measure of an n-variable family
JO - Acta Arithmetica
PY - 2016
VL - 174
IS - 1
SP - 1
EP - 30
AB - 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.
LA - eng
KW - Mahler measure; higher Mahler measure; special values of $\zeta $(s) and Dirichlet L-functions; polylogarithms
UR - http://eudml.org/doc/286323
ER -