On the Mahler measure of (1+x)(1+y)+z
Abstract
We prove a conjecture of Boyd and Rodriguez Villegas relating the Mahler measure of the polynomial (1+x)(1+y)+z and the value at s=3 of the L-function of an elliptic curve of conductor 15. The proof makes use of the computation by Zudilin and the author of the regulator of certain K4 classes on modular curves.
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