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

2023/01/16 by Giacomo Cherubini, Pavlo Yatsyna, Cherubini, Giacomo +1 · 1 citation
Computer Science · #11C08 (Secondary) #11R06 (Primary) 11Y40 #11R09 #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic, programming, and type systems #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2301.06536

openalex publication_date 2023/01/16 · openalex created_date 2023/02/15 · openalex updated_date 2026/07/28

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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• The Minimal Degree of Salem Numbers with Negative Trace

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