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The elliptic trilogarithm and Mahler measures of $K3$ surfaces (1309.7730v2)

Published 30 Sep 2013 in math.NT

Abstract: The aim of this paper is to derive explicitly a connection between the Zagier elliptic trilogarithm and Mahler measures of a certain family of three-variable polynomials defining K3 surfaces. In addition, we prove some linear relations satisfied by the elliptic trilogarithm evaluated at torsion points on elliptic curves. This result can be viewed as a higher dimensional analogue of exotic relations of the elliptic dilogarithm.

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