On stable polynomials of degrees 2,3,4

2023/04/08 by Tong Lin, Qiang Wang, Lin, Tong +1
Computer Science · Mathematics · #11B37 #11T06 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2304.03992

openalex publication_date 2023/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let q be a prime power. We construct stable polynomials of the form b^m-1(x+a)^m+c(x+a)+d over a finite field \mathbbF_q for m=2,3,4 by Capelli's lemma. When m=3 and q is even, we confirm the conjecture of Ahmadi and Monsef-Shokri [2] that the polynomial f(x) = x³ + x² + 1 is stable over \mathbbF₂. Moreover, when m=2 and q≡ 1\pmod4, we improve a lower bound of the number of quadratic stable polynomials by Goméz-Pérez and Nicolás [4].

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