The elliptic trilogarithm and Mahler measures of K3 surfaces
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Detchat Samart
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.
© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- The elliptic trilogarithm and Mahler measures of K3 surfaces
- Morphisms determined by objects and flat covers
- Graev ultrametrics and free products of Polish groups
- Critical values of Rankin–Selberg L-functions for GLn × GLn-1 and the symmetric cube L-functions for GL2
- Simple connectivity in polar spaces
- On the μ-invariant of Katz p-adic L-functions attached to imaginary quadratic fields
- Non-existence of certain Einstein metrics on some symplectic manifolds
- A note on real algebraic groups
- Coercive and noncoercive nonlinear Neumann problems with indefinite potential
- No universal group in a cardinal
- Finite involution semigroups with infinite irredundant bases of identities
Articles in the same Issue
- Frontmatter
- The elliptic trilogarithm and Mahler measures of K3 surfaces
- Morphisms determined by objects and flat covers
- Graev ultrametrics and free products of Polish groups
- Critical values of Rankin–Selberg L-functions for GLn × GLn-1 and the symmetric cube L-functions for GL2
- Simple connectivity in polar spaces
- On the μ-invariant of Katz p-adic L-functions attached to imaginary quadratic fields
- Non-existence of certain Einstein metrics on some symplectic manifolds
- A note on real algebraic groups
- Coercive and noncoercive nonlinear Neumann problems with indefinite potential
- No universal group in a cardinal
- Finite involution semigroups with infinite irredundant bases of identities
