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From L-series of elliptic curves to Mahler measures

  • Mathew Rogers (a1) and Wadim Zudilin (a2)

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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References

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From L-series of elliptic curves to Mahler measures

  • Mathew Rogers (a1) and Wadim Zudilin (a2)

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