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arXiv · 1710.04602

Mahler measures of elliptic modular surfaces

Francois Brunault·Michael Neururer
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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.

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Francois Brunault, Michael Neururer. 2017-10-12. Mahler measures of elliptic modular surfaces. https://doi.org/10.1090/tran%2F7524

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