On the Mahler measure of $(1+x)(1+y)+z$

François Brunault

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arXiv · 2305.02992

On the Mahler measure of $(1+x)(1+y)+z$

François Brunault

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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.

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François Brunault. 2023-05-04. On the Mahler measure of $(1+x)(1+y)+z$. https://arxiv.org/abs/2305.02992

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