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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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https://hal-ens-lyon.archives-ouvertes.fr/ensl-01953103
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Submitted on : Wednesday, December 12, 2018 - 4:09:05 PM
Last modification on : Wednesday, December 4, 2019 - 4:04:27 PM
Long-term archiving on: : Wednesday, March 13, 2019 - 3:10:37 PM

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

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