Mahler measures of elliptic modular surfaces
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- by François Brunault and Michael Neururer PDF
- Trans. Amer. Math. Soc. 372 (2019), 119-152 Request permission
Abstract:
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’s, 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.References
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Additional Information
- François Brunault
- Affiliation: ÉNS Lyon, UMPA, 46 allée d’Italie, 69007 Lyon, France
- Email: francois.brunault@ens-lyon.fr
- Michael Neururer
- Affiliation: TU Darmstadt, Schloßgartenstr. 7, 64289 Darmstadt, Germany
- MR Author ID: 1160909
- Email: neururer@mathematik.tu-darmstadt.de
- Received by editor(s): October 18, 2017
- Received by editor(s) in revised form: February 5, 2018
- Published electronically: September 24, 2018
- Additional Notes: The second author was supported by EPSRC grant N007360, “Explicit methods for Jacobi forms over number fields", and the DFG Forschergruppe-1920.
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 119-152
- MSC (2010): Primary 11R06; Secondary 11F67, 14J27, 19F27
- DOI: https://doi.org/10.1090/tran/7524
- MathSciNet review: 3968765