From L-series of elliptic curves to Mahler measures

@article{Rogers2012FromLO,
  title={From L-series of elliptic curves to Mahler measures},
  author={Mathew Rogers and Wadim Zudilin},
  journal={Compositio Mathematica},
  year={2012},
  volume={148},
  pages={385 - 414}
}
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. 
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