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 for Kuga-Sato varieties, to arrive at an L-value.
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Submitted on : Wednesday, December 12, 2018 - 4:09:05 PM
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François Brunault, Michael Neururer. Mahler measures of elliptic modular surfaces. Transactions of the American Mathematical Society, American Mathematical Society, In press. ⟨ensl-01953103⟩

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