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

Huimin Zheng; Xuejun Guo; Hourong Qin; Huimin Zheng; Xuejun Guo; Hourong Qin

doi:10.3934/era.2020007

Electronic Research Archive

2020, Volume 28, Issue 1: 103-125. doi: 10.3934/era.2020007

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

Department of Mathematics, Nanjing Univeristy, Nanjing, Jiangsu 210093, China

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].
- Mahler measure,
- modular forms,
- Dirichlet series,
- L-functions,
- Hecke charactors
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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Abstract

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].

References

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