2024/02/12 by Toufik Zaimi, Zaimi, Toufik
Computer Science · Mathematics · #11R04 #11R06 #11Y40 #Advanced Algebra and Logic #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2402.07481
openalex publication_date 2024/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that for any natural number n satisfying n≡ 4 \mod 8 and n\not≡ 0 \mod 5, and for any odd integer t≥ (n+6)/(2) there are infinitely many Salem numbers α of degree 2t such that αn-1 is a unit. This result, obtained using a generalization of a construction due to Gross and McMullen [5], partially completes the main result of [7].