Mahler measure and elliptic curve L-functions at s = 3
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Matilde Lalín
Abstract
We study the Mahler measure of some three-variable polynomials that are conjectured to be related to L-functions of elliptic curves at s = 3 by Boyd. The connection with L-functions can be explained with the use of a regulator and a result of Goncharov. Finally, we prove a relationship between two formulas.
The author is very grateful to David Boyd for generously sharing his numerical examples with her and for many stimulating discussions regarding this project and related ideas. The author thanks Wadim Zudilin and Mathew Rogers for several useful comments and corrections and enthusiastic discussions about this and related topics. Finally, the author is grateful to the referee for corrections and invaluable comments that have greatly improved the exposition of this paper. This work was supported by the Natural Sciences and Engineering Research Council of Canada (Discovery Grant 355412-2008) and the Fonds de recherche du Québec – Nature et technologies (Établissement de nouveaux chercheurs 144987 and Projet de recherche en équipe 166534).
© 2015 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- The limit of the Yang–Mills flow on semi-stable bundles
- Tangent cones to positive-(1,1) De Rham currents
- A characterization of vertex operator algebras V+ℤα: I
- Degenerate neckpinches in Ricci flow
- On the local Bump–Friedberg L-function
- A variational characterization of J-holomorphic curves
- Mahler measure and elliptic curve L-functions at s = 3
- Uniform bounds for bounded geodesic image theorems
- Linear stability of Perelman's ν-entropy on symmetric spaces of compact type
Artikel in diesem Heft
- Frontmatter
- The limit of the Yang–Mills flow on semi-stable bundles
- Tangent cones to positive-(1,1) De Rham currents
- A characterization of vertex operator algebras V+ℤα: I
- Degenerate neckpinches in Ricci flow
- On the local Bump–Friedberg L-function
- A variational characterization of J-holomorphic curves
- Mahler measure and elliptic curve L-functions at s = 3
- Uniform bounds for bounded geodesic image theorems
- Linear stability of Perelman's ν-entropy on symmetric spaces of compact type
