Electronic Research Archive

2020, Issue 1: 103-125. doi: 10.3934/era.2020007

The Mahler measure of $(x+1/x)(y+1/y)(z+1/z)+\sqrt{k}$

• Received: 01 October 2019 Revised: 01 December 2019
• Primary: 11F67, 11R06; Secondary: 33C20

• In this paper we study the Mahler measures of reciprocal polynomials $(x+1/x)(y+1/y)(z+1/z)+\sqrt{k}$ for $k = 16$, $k = -104\pm60\sqrt{3}$, $4096$ and $k = -2024\pm765\sqrt{7}$. We prove six conjectural identities proposed by Samart in [16].

Citation: Huimin Zheng, Xuejun Guo, Hourong Qin. The Mahler measure of $(x+1/x)(y+1/y)(z+1/z)+\sqrt{k}$[J]. Electronic Research Archive, 2020, 28(1): 103-125. doi: 10.3934/era.2020007

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• In this paper we study the Mahler measures of reciprocal polynomials $(x+1/x)(y+1/y)(z+1/z)+\sqrt{k}$ for $k = 16$, $k = -104\pm60\sqrt{3}$, $4096$ and $k = -2024\pm765\sqrt{7}$. We prove six conjectural identities proposed by Samart in [16].

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