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Journal Articles Transactions of the American Mathematical Society Year : 2019

Mahler measures of elliptic modular surfaces

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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 for Kuga-Sato varieties, to arrive at an L-value.
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Dates and versions

ensl-01953103 , version 1 (12-12-2018)

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François Brunault, Michael Neururer. Mahler measures of elliptic modular surfaces. Transactions of the American Mathematical Society, 2019, 372, pp.119-152. ⟨10.1090/tran/7524⟩. ⟨ensl-01953103⟩
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