Abstract
We prove that there exist Salem numbers with trace –3 and every even degree ≥ 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 ≤ 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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