N. Carella

collaborators

5 papers

math.GM2026

Least Consecutive Pair of Primitive Roots

N. A. Carella

Let $p > 1$ be a large prime number and let $x = O ((lo g p)^{2} (lo g lo g p)^{5}$ be a real number. It is proved that the least consecutive pair of primitive roots $u \neq = \pm 1, v^{2}$ and $u + 1$ …

math.GM2026

Equidistribution of Primitive Normal Elements in Finite Fields

N. A. Carella

Let $q = p^{k}$ be a prime power, let $n \geq 2$ be an integer and let $F_{q^{n}}$ be a finite field. It is shown that the set of primitive normal elements is a Salem set. Further…

math.GM2026

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

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

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…