English

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