Mahler’s Measure and the Dilogarithm (I)

  title={Mahler’s Measure and the Dilogarithm (I)},
  author={David W. Boyd and Fernando Rodriguez-Villegas},
  journal={Canadian Journal of Mathematics},
  pages={468 - 492}
Abstract 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. 
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