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A Generalization of a Theorem of Boyd and Lawton

Published online by Cambridge University Press:  20 November 2018

Zahraa Issa  and
Matilde Lalín
Zahraa Issa
Affiliation:
Département de mathématiques et de statistique, Université de Montréal, Montreal, QC H3C 3J7 e-mail: issaz@dms.umontreal.camlalin@dms.umontreal.ca
Matilde Lalín
Affiliation:
Département de mathématiques et de statistique, Université de Montréal, Montreal, QC H3C 3J7 e-mail: issaz@dms.umontreal.camlalin@dms.umontreal.ca
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Abstract.

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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 ${{\log }^{k}}\,\left| P \right|$).

Keywords

11R0611R09Mahler measurepolynomial
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 4 , 01 December 2013 , pp. 759 - 768
Copyright
Copyright © Canadian Mathematical Society 2013

References

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