Salem numbers of negative trace

Smyth, C.

doi:10.1090/S0025-5718-99-01099-6

Salem numbers of negative trace
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by C. J. Smyth PDF

Math. Comp. 69 (2000), 827-838 Request permission

Abstract:

We prove that, for all $d\geq 4$, there are Salem numbers of degree $2d$ and trace $-1$, and that the number of such Salem numbers is $\gg d/\left ( \log \log d\right ) ^{2}$. As a consequence, it follows that the number of totally positive algebraic integers of degree $d$ and trace $2d-1$ is also $\gg d/\left ( \log \log d\right ) ^{2}$.

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