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

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

2010-12-14

arxiv.org/abs/1012.3036v3

Compositio Mathematica 148 (2012), no. 2, 385-414

Mathematics

Number Theory

33 pages

Scientific paper

10.1112/S0010437X11007342

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 $(1+X)(1+Y)(X+Y)-\alpha XY$, $\alpha\in\mathbb R$.

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