Taiwanese Journal of Mathematics

Finding All Salem Numbers of Trace $-1$ and Degree up to $20$

Youyan Chen, Chenggang Peng, and Qiang Wu

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In 1999, C. J. Smyth proved that, for all $d \geq 4$, there are Salem numbers of degree $2d$ and trace $-1$, and that the number of them is greater than $0.1387d/(\log \log d)^2$. He gave also all Salem numbers of trace $-1$ and degree $2d = 8,10,12,14$. In this paper, we complete the table of the minimal polynomials of all Salem numbers of trace $-1$ and degree $2d = 16, 18, 20$, and we conjecture a new lower bound of the numbers of such Salem numbers.

Article information

Taiwanese J. Math., Volume 22, Number 1 (2018), 23-37.

Received: 16 August 2016
Revised: 18 April 2017
Accepted: 30 July 2017
First available in Project Euclid: 4 October 2017

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Zentralblatt MATH identifier

Primary: 11R06: PV-numbers and generalizations; other special algebraic numbers; Mahler measure

algebraic integer Salem number explicit auxiliary function integer transfinite diameter


Chen, Youyan; Peng, Chenggang; Wu, Qiang. Finding All Salem Numbers of Trace $-1$ and Degree up to $20$. Taiwanese J. Math. 22 (2018), no. 1, 23--37. doi:10.11650/tjm/8208. https://projecteuclid.org/euclid.twjm/1507082438

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