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arXiv · 1012.3036

From $L$-series of elliptic curves to Mahler measures

Mathew Rogers·Wadim Zudilin
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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 CM elliptic curves of conductors 27 and 36. Furthermore, we prove a new functional equation for the Mahler measure of the polynomial family $(1+X)(1+Y)(X+Y)-αXY$, $α\in\mathbb R$.

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Mathew Rogers, Wadim Zudilin. 2011-09-30. From $L$-series of elliptic curves to Mahler measures. https://doi.org/10.1112/s0010437x11007342

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