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arXiv · 2301.06536

There are Salem numbers with trace $-3$ and every degree at least $34$

Giacomo Cherubini·Pavlo Yatsyna
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Abstract

We prove that there exist Salem numbers with trace $-3$ and every even degree $\geq 34$. Our proof combines a theoretical approach, which allows us to treat all sufficiently large degrees, with a numerical search for small degrees. Since it is known that there are no Salem numbers of trace $-3$ and degree $\leq 30$, our result is optimal up to possibly the single value $32$, for which it is expected there are no such numbers.

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Giacomo Cherubini, Pavlo Yatsyna. 2023-01-16. There are Salem numbers with trace $-3$ and every degree at least $34$. https://arxiv.org/abs/2301.06536

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