Open Access
February, 2018 Finding All Salem Numbers of Trace $-1$ and Degree up to $20$
Youyan Chen, Chenggang Peng, Qiang Wu
Taiwanese J. Math. 22(1): 23-37 (February, 2018). DOI: 10.11650/tjm/8208


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.


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Youyan Chen. Chenggang Peng. Qiang Wu. "Finding All Salem Numbers of Trace $-1$ and Degree up to $20$." Taiwanese J. Math. 22 (1) 23 - 37, February, 2018.


Received: 16 August 2016; Revised: 18 April 2017; Accepted: 30 July 2017; Published: February, 2018
First available in Project Euclid: 4 October 2017

zbMATH: 06965357
MathSciNet: MR3749352
Digital Object Identifier: 10.11650/tjm/8208

Primary: 11R06

Keywords: Algebraic integer , explicit auxiliary function , integer transfinite diameter , Salem number

Rights: Copyright © 2018 The Mathematical Society of the Republic of China

Vol.22 • No. 1 • February, 2018
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