Mahler measures of elliptic modular surfaces

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.

Revised version with a new Mahler measure for the elliptic surface E(4). The article will appear in Transactions of the AMS

References in corpus (3)

• Mahler measures and computations with regulators
• Mahler measure of some singular K3-surfaces
• Régulateurs modulaires explicites via la méthode de Rogers-Zudilin

Cited by in corpus (2)

• Volume function and Mahler measure of exact polynomials
• Mahler Measure of 3D Landau-Ginzburg Potentials