The elliptic trilogarithm and Mahler measures of K3 surfaces

2013/09/30 by Detchat Samart, Samart, Detchat
Mathematics · #11G55 #FOS: Mathematics #Number Theory (math.NT) #Primary: 11F67 Secondary: 33C20 #math.NT #msc:11F67 #msc:11G55 #msc:33C20

paper · pdf · doi:10.48550/arxiv.1309.7730

25 pages

arxiv created 2014/03/15 · arxiv updated 2014/03/18

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.

Related

• Mahler measure of some singular K3-surfaces
• The Mahler measure of exact polynomials in three variables
• The Mahler measure of exact polynomials and special L-values of K3 surfaces
• The Mahler measure and the L-series of a singular K3-surface
• CM points, class numbers, and the Mahler measures of x³+y³+1-kxy