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2 results on '"Primary: 11F67 Secondary: 33C20, 11G55"'

1. The elliptic trilogarithm and Mahler measures of $K3$ surfaces

Author

Samart, Detchat

Subjects
Mathematics - Number Theory, Primary: 11F67 Secondary: 33C20, 11G55
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., Comment: 25 pages

Published
2013

2. The elliptic trilogarithm and Mahler measures of K3 surfaces

Author

Detchat Samart

Subjects
Pure mathematics, Quarter period, Mathematics - Number Theory, Applied Mathematics, General Mathematics, 010102 general mathematics, Mathematical analysis, 0102 computer and information sciences, Primary: 11F67 Secondary: 33C20, 11G55, 01 natural sciences, Supersingular elliptic curve, Jacobi elliptic functions, Elliptic curve, 010201 computation theory & mathematics, Mahler measure, FOS: Mathematics, Torsion (algebra), Elliptic rational functions, Number Theory (math.NT), 0101 mathematics, Schoof's algorithm, Mathematics
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., 25 pages

Published
2015

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