On the minimal number of small elements generating prime field

2017/03/20 by Marc Munsch, Munsch, Marc
Computer Science · Mathematics · #11A07 #11A15 #11L40 #11N36 #11T99 #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1703.06673

openalex publication_date 2017/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we give an upper bound for the number of elements from the interval [1,p^1/4e^1/2+ε] necessary to generate the finite field \mathbbF_p with p an odd prime.

Related

• Four consecutive primitive elements in a finite field
• Finding Primitive Elements in Finite Fields of Small Characteristic
• Small Primitive Normal Elements in Finite Fields
• On primitive elements in finite fields of low characteristic
• On the construction of small subsets containing special elements in a finite field