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# A Mahler Measure of a $K3$ Surface Expressed as a Dirichlet $L$-Series

Published:2011-04-14
Printed: Mar 2012
• Marie José Bertin,
Université Pierre et Marie Curie (Paris 6), Institut de Mathématiques, 175 rue du Chevaleret, 75013 Paris
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## Abstract

We present another example of a $3$-variable polynomial defining a $K3$-hypersurface and having a logarithmic Mahler measure expressed in terms of a Dirichlet $L$-series.
 Keywords: modular Mahler measure, Eisenstein-Kronecker series, $L$-series of $K3$-surfaces, $l$-adic representations, Livné criterion, Rankin-Cohen brackets
 MSC Classifications: 11 - unknown classification 1114D - unknown classification 14D14J - unknown classification 14J

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