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Mahler’s Measure and the Dilogarithm (I)

Published online by Cambridge University Press:  20 November 2018

David W. Boyd  and
Fernando Rodriguez-Villegas
David W. Boyd
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, British Columbia, V6T 1Z2, e-mail: boyd@math.ubc.ca
Fernando Rodriguez-Villegas
Affiliation:
Department of Mathematics, University of Texas at Austin, Austin, Texas, 78712 USA, e-mail: villegas@math.utexas.edu
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Abstract

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An explicit formula is derived for the logarithmic Mahler measure $m(P)$ of $P(x,\,y)\,=\,P(x)y-q(x)$, where $p(x)$ and $q(x)$ are cyclotomic. This is used to find many examples of such polynomials for which $m(P)$ is rationally related to the Dedekind zeta value ${{\text{ }\!\!\zeta\!\!\text{ }}_{F}}(2)$ for certain quadratic and quartic fields.

Keywords

11G4011R0611Y35
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 54 , Issue 3 , 01 June 2002 , pp. 468 - 492
Copyright
Copyright © Canadian Mathematical Society 2002

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