Year: 2025
Type: article
Abstract: Let p > 1 p\gt 1 be a large prime number, and let ε > 0 \varepsilon \gt 0 be a small number. The established unconditional upper bounds of the least primitive root u ≠ ± 1 , v 2 u\ne \pm 1,{v}^{2} in the prime finite field F p {{\mathbb{F}}}_{p} have exponential magnitudes u ≪ p 1 ⁄ 4 + ε u\ll {p}^{1/4+\varepsilon } . This note contributes a new result to the literature. It proves that the upper bound of the least primitive root has polynomial magnitude u ≤ ( log p ) 1 + ε u\le {\left(\log p)}^{1+\varepsilon } unconditionally.
Author: Nelson Carella
Institution: Fordham University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,187
OpenAlex ID: W4409064183