Exercising in complex Mahler measures: diamonds are not forever
Number Theory
2021-10-12 v2 Classical Analysis and ODEs
Complex Variables
K-Theory and Homology
Abstract
Recently, Hang Liu and Hourong Qin came up with a numerical observation about the relation between the Mahler measures of one hyperelliptic and two elliptic families. The discoverers foresee a proof of the identities "by extending ideas in" two papers of Matilde Lal\'{\i}n and Gang Wu, the ideas based on a theorem of Spencer Bloch and explicit diamond-operation calculations on the underlying curves. We prove the relation using the already available diamond-free methodology. While finding such relations for the Mahler measures remains an art, proving them afterwards is mere complex (analysis) exercising.
Cite
@article{arxiv.2109.14380,
title = {Exercising in complex Mahler measures: diamonds are not forever},
author = {Berend Ringeling and Wadim Zudilin},
journal= {arXiv preprint arXiv:2109.14380},
year = {2021}
}
Comments
5 pages