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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-José Bertin. In(More)
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