A Mahler measure of a K3-hypersurface expressed as a Dirichlet L-series

TL;DR

This paper provides an example of a K3-hypersurface defined by a 3-variable polynomial whose Mahler measure can be explicitly expressed as a Dirichlet L-series, illustrating a deep connection between algebraic geometry and number theory.

Contribution

It introduces a new example linking Mahler measures of K3-hypersurfaces to Dirichlet L-series, expanding known cases of such relationships.

Findings

Mahler measure expressed as a Dirichlet L-series

New example of K3-hypersurface with this property

Strengthens links between algebraic geometry and number theory

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.