N. Carella

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20242026

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math.GM2025

Small Prime Primitive Roots in Arithmetic Progressions

N. A. Carella

Let $p > 1$ be a large prime number, let $q = O (lo g lo g p)$ and let $1 \leq a < q$ be a pair of relatively prime integers. It is proved that there is a prime primitive root $u\ll (\log p…

math.GM2025

Small Primitive Normal Elements in Finite Fields

N. A. Carella

Let $q = p^{k}$ be a prime power, let $F_{q}$ be a finite field and let $n \geq 2$ be an integer. This note investigates the existence small primitive normal elements in finite fi…

math.GM2025

Simultaneous Primitive Roots over Finite Rings

N. A. Carella

This note investigates the average density of prime numbers $p \in [x, 2 x]$ with respect to a random simultaneous primitive root $g \leq p^{1/2 + ε}$ over the finite rings $\ma…