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

&lt;abstract&gt;&lt;p&gt;In this paper we study the Mahler measures of reciprocal polynomials &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ (x+1/x)(y+1/y)(z+1/z)+\sqrt{k} $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; for &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$ k = 16 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;, &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}$ k = -104\pm60\sqrt{3} $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;, &lt;inline-formula&gt;&lt;tex-math id="M5"&gt;\begin{document}$ 4096 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; and &lt;inline-formula&gt;&lt;tex-math id="M6"&gt;\begin{document}$ k = -2024\pm765\sqrt{7} $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;. We prove six conjectural identities proposed by Samart in [&lt;xref ref-type="bibr" rid="b16"&gt;16&lt;/xref&gt;].&lt;/p&gt;&lt;/abstract&gt;

Locations

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