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Accessible Unlicensed Requires Authentication Published by De Gruyter January 13, 2015

The elliptic trilogarithm and Mahler measures of K3 surfaces

Detchat Samart
From the journal Forum Mathematicum

Abstract

The aim of this paper is to derive explicitly a connection between the Zagier elliptic trilogarithm and Mahler measures of certain families 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.

Funding source: NSF

Award Identifier / Grant number: DMS-1200577

Funding statement: The author's research was partially supported by NSF Grant DMS-1200577.

The author would like to thank Ken Ono for his encouragement during the author's visit at Emory University in the spring semester 2013. His comments and suggestions significantly led to a motivation to continue this research project. The author also thanks Matthew Papanikolas for several helpful discussions and the anonymous referees for their insightful and useful comments which helped to improve the exposition of this paper.

Received: 2014-3-15
Revised: 2014-7-26
Published Online: 2015-1-13
Published in Print: 2016-5-1

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