Mahler measure of some singular K3-surfaces
Number Theory
2012-08-31 v1
Abstract
We study the Mahler measure of the three-variable Laurent polynomial x + 1/x + y + 1/y + z + 1/z - k where k is a parameter. The zeros of this polynomial define (after desingularization) a family of K3-surfaces. In favorable cases, the K3-surface has Picard number 20, and the Mahler measure is related to its L-function. This was first studied by Marie-Jose Bertin. In this work, we prove several new formulas, extending the earlier work of Bertin.
Cite
@article{arxiv.1208.6240,
title = {Mahler measure of some singular K3-surfaces},
author = {Marie-Jose Bertin and Amy Feaver and Jenny Fuselier and Matilde Lalin and Michelle Manes},
journal= {arXiv preprint arXiv:1208.6240},
year = {2012}
}
Comments
17 pages