N. Carella

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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.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…

math.GM2024

Density of Squarefree Totients $p - 1$ and Primitive Roots

N. A. Carella

This note determines an effective asymptotic formula for the number of squarefree totients $p - 1$ with a fixed primitive root $u \neq = \pm 1, v^{2}$ .

math.GM2024

Legendre Conjecture over Arithmetic Progressions

N. A. Carella

Let $1 \leq a < q$ be a pair of small integers such that $g cd (a, q) = 1$ and let $x > 1$ be a large number. This note discusses the existence of a short sequence of primes $p\equiv a\bmod…

Least Consecutive Pair of Primitive Roots

Equidistribution of Primitive Normal Elements in Finite Fields

Small Prime Primitive Roots in Arithmetic Progressions

Small Primitive Normal Elements in Finite Fields

Simultaneous Primitive Roots over Finite Rings

Density of Squarefree Totients p−1 and Primitive Roots

Legendre Conjecture over Arithmetic Progressions

Density of Squarefree Totients $p - 1$ and Primitive Roots