The elliptic trilogarithm and Mahler measures of $K3$ surfaces
Number Theory
2014-03-18 v2
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.
Keywords
Cite
@article{arxiv.1309.7730,
title = {The elliptic trilogarithm and Mahler measures of $K3$ surfaces},
author = {Detchat Samart},
journal= {arXiv preprint arXiv:1309.7730},
year = {2014}
}
Comments
25 pages