English

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.

Keywords

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}
}

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17 pages