Mahler measures of elliptic modular surfaces
Number Theory
2023-06-23 v2
Abstract
In this article we develop a new method for relating Mahler measures of three-variable polynomials that define elliptic modular surfaces to L-values of modular forms. Using an idea of Deninger, we express the Mahler measure as a Deligne period of the surface and then apply the first author's extension of the Rogers-Zudilin method to Kuga-Sato varieties to arrive at an L-value.
Keywords
Cite
@article{arxiv.1710.04602,
title = {Mahler measures of elliptic modular surfaces},
author = {Francois Brunault and Michael Neururer},
journal= {arXiv preprint arXiv:1710.04602},
year = {2023}
}
Comments
Revised version with a new Mahler measure for the elliptic surface E(4). The article will appear in Transactions of the AMS