The Mahler measure and the L-series of a singular K3-surface

TL;DR

This paper provides the first example linking the Mahler measure of a polynomial defining a singular K3-surface to its Newton polyhedron faces and the surface's L-series, advancing understanding in algebraic geometry and number theory.

Contribution

It introduces a novel explicit connection between Mahler measures and L-series for a singular K3-surface, a previously unestablished relationship.

Findings

Mahler measure expressed via Newton polyhedron faces

Connection established between Mahler measure and L-series

First explicit example of this relationship in singular K3-surfaces

Abstract

We present the first example of a polynomial defining a singular K3-surface whose Mahler measure is expressed in terms of the Mahler measure of the faces of its Newton polyhedron and the L-series of the K3-surface.