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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