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 $K_4$ classes on modular curves.

arXiv comment12 pages, with tables in an appendix