From L-series of Elliptic Curves to Mahler Measures
نویسندگان
چکیده
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 ∈ R.
منابع مشابه
Transformations of L-values
In our recent work with M. Rogers on resolving some Boyd’s conjectures on two-variate Mahler measures, a new analytical machinery was introduced to write the values L(E, 2) of L-series of elliptic curves as periods in the sense of Kontsevich and Zagier. Here we outline, in slightly more general settings, the novelty of our method with Rogers, and provide a simple illustrative example. Throughou...
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