The Mahler measure of <inline-formula><tex-math id="M1">$ (x+1/x)(y+1/y)(z+1/z)+\sqrt{k} $</tex-math></inline-formula>
The Mahler measure of <inline-formula><tex-math id="M1">$ (x+1/x)(y+1/y)(z+1/z)+\sqrt{k} $</tex-math></inline-formula>
<abstract><p>In this paper we study the Mahler measures of reciprocal polynomials <inline-formula><tex-math id="M2">\begin{document}$ (x+1/x)(y+1/y)(z+1/z)+\sqrt{k} $\end{document}</tex-math></inline-formula> for <inline-formula><tex-math id="M3">\begin{document}$ k = 16 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M4">\begin{document}$ k = -104\pm60\sqrt{3} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ 4096 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$ k = -2024\pm765\sqrt{7} $\end{document}</tex-math></inline-formula>. We prove six conjectural identities proposed by Samart in [<xref ref-type="bibr" …