Mahler measure of some singular K3-surfaces

2012/08/30 by Marie-Jose Bertin, Bertin, Marie-Jose, Amy Feaver +7
Mathematics · #14J27 #14J28 #FOS: Mathematics #Number Theory (math.NT) #Primary 11R06 #Secondary 11R09 #math.NT #msc:11R06 #msc:11R09 #msc:14J27 #msc:14J28

paper · pdf · doi:10.48550/arxiv.1208.6240

17 pages

arxiv created 2012/08/30 · arxiv updated 2012/08/31

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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