On algebraic integers which are 2-Salem elements in positive characteristic

2020/12/31 by Mabrouk Ben Nasr, Nasr, Mabrouk, Hassen Kthiri +3
Computer Science · Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Logic, programming, and type systems #Number Theory (math.NT) #semigroups and automata theory

paper · doi:10.48550/arxiv.2012.15539

openalex publication_date 2020/12/31 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Bateman and Duquette have initiated the study of Salem elements in positive characteristic. This work extends their results to 2-Salem elements whose minimal polynomials are of the type Yⁿ + λ_n-1Y^n-1 + …+λ₁Y + λ₀ ∈ \mathbbF_q[X][Y ] where n ≥2, λ₀≠ 0 and °λ_n-1 < °λ_n-2 = max_{i≠ n-2}°(λ_i). This work provides an analogue of their results for 2-Salem elements whose minimal polynomials meet certain requirements.

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