Three-variable Mahler measures and special values of modular and Dirichlet $L$-series

Detchat Samart

In this paper we prove that the Mahler measures of the Laurent polynomials $(x+x^{-1})(y+y^{-1})(z+z^{-1})+k$, $(x+x^{-1}{)}^2(y+y^{-1}{)}^2(1+z{)}^3{z}^{-2}-k$, and $x^4+y^4+z^4+1+k^{1/4}…