Existence of Special Types Primitive Pairs in Finite Fields Avoiding Affine Hyperplanes

2024/12/11 by Himangshu Hazarika, Hazarika, Himangshu, Giorgos Kapetanakis +3
Engineering · Mathematics · Computer Science · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2412.08455

Abstract

Let \Fm be finite fields of order q^m, where m≥ 2 and q, a prime power. Given \F-affine hyperplanes A₁,…, A_m of \Fm in general position, we study the existence of primitive element α of \Fm, such that f(α) is also primitive, where ax²+bx+c∈ \Fm[x] (a≠ 0 and b²≠ 4ac) in \Fm and the primitive pair (α, f(α)) avoids each A_i. We establish results for fields of higher order.

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