From L-series of elliptic curves to Mahler measures

By Mathew Rogers, Wadim Zudilin. Compositio Mathematica, 2010

72 citations recorded by the source corpus.

Abstract We prove the conjectural relations between Mahler measures and L-values of elliptic curves of conductors 20 and 24. We also present new hypergeometric expressions for L-values of elliptic curves of conductors 27 and 36. Furthermore, we prove a new functional equation for the Mahler measure of the polynomial family (1+X) (1+Y )(X+Y )−αXY, α∈ℝ.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ad7a532ca71abac6704ff914fa52df1f7fee5d67