Salem numbers with minimal trace

Chen, Qiong; Wu, Qiang

doi:10.1090/mcom/3833

Salem numbers with minimal trace
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by Qiong Chen and Qiang Wu HTML | PDF

Math. Comp. 92 (2023), 1779-1790 Request permission

Abstract:

In this paper, a new method to compute lower and upper bounds for Salem numbers with a given trace and a given degree is given. With this method, it is proven that the smallest trace of Salem numbers of degree $22$ is $-1$. Further, new lower bounds for degree of Salem numbers with minimal trace $-5$ and $-6$ are given. All Salem numbers of trace $-2$ and degree $24$, $26$ are given. This includes $7$ additional Salem numbers of degree $26$ beyond what was previously known. The auxiliary functions related to Chebyshev polynomials, which are adapted to Salem number, are used in this work.

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