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arXiv · 1208.6240

Mahler measure of some singular K3-surfaces

Marie-Jose Bertin·Amy Feaver·Jenny Fuselier·Matilde Lalin·Michelle Manes
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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.

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Marie-Jose Bertin, Amy Feaver, Jenny Fuselier, Matilde Lalin, Michelle Manes. 2012-08-30. Mahler measure of some singular K3-surfaces. https://arxiv.org/abs/1208.6240

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