A Generalization of a Theorem of Boyd and Lawton
Canadian mathematical bulletin, Tome 56 (2013) no. 4, pp. 759-768
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The Mahler measure of a nonzero $n$ -variable polynomial $P$ is the integral of $\log \,\left| P \right|$ on the unit $n$ -torus. A result of Boyd and Lawton says that the Mahler measure of a multivariate polynomial is the limit of Mahler measures of univariate polynomials. We prove the analogous result for different extensions of Mahler measure such as generalized Mahler measure (integrating the maximum of $\log \,\left| P \right|$ for possibly different ${{P}^{'}}\text{s}$ ), multiple Mahler measure (involving products of $\log \,\left| P \right|$ for possibly different ${{P}^{'}}\text{s}$ ), and higher Mahler measure (involving ${{\log }^{k}}\,\left| P \right|$ ).
Issa, Zahraa; Lalín, Matilde. A Generalization of a Theorem of Boyd and Lawton. Canadian mathematical bulletin, Tome 56 (2013) no. 4, pp. 759-768. doi: 10.4153/CMB-2012-010-2
@article{10_4153_CMB_2012_010_2,
author = {Issa, Zahraa and Lal{\'\i}n, Matilde},
title = {A {Generalization} of a {Theorem} of {Boyd} and {Lawton}},
journal = {Canadian mathematical bulletin},
pages = {759--768},
year = {2013},
volume = {56},
number = {4},
doi = {10.4153/CMB-2012-010-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-010-2/}
}
TY - JOUR AU - Issa, Zahraa AU - Lalín, Matilde TI - A Generalization of a Theorem of Boyd and Lawton JO - Canadian mathematical bulletin PY - 2013 SP - 759 EP - 768 VL - 56 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-010-2/ DO - 10.4153/CMB-2012-010-2 ID - 10_4153_CMB_2012_010_2 ER -
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