N. Carella

activity

20052026

most citedPrime Values of Quadratic Polynomials

2 citations · 23 across the 94 of their papers we have counts for

collaborators

95 papers

math.GM2026

Note on the Exceptional Set in the ABC Conjecture

N. A. Carella

Fix $ε > 0$ , let $x > 1$ be a large real number and let $rad (n) = \prod_{p ∣ n} p$ be the radical of an integer $n \geq 1$ . A triple $(a, b, c)$ , with $a + b = c$ and $\gcd(a,b…

math.GM2024

Small Prime $k$ th Power Residues and Nonresidues in Arithmetic Progressions

N. A. Carella

Let $p$ be a large odd prime, let $x = lo g p) (lo g lo g p)^{3 + ε}$ and let $q ≪ lo g lo g p$ be an integer, where $ε > 0$ is a small number. This note proves the exis…

math.GM2023

Largest Prime Factors of Polynomials

N. A. Carella

Let $x > 1$ be a large number. This note shows that the largest prime factor of the quadratic product $\prod_{x \leq n \leq 2 x} (n^{2} + 1)$ satisfies the relation $p \geq x^{3/…

math.GM2023★ 1 cited

Note on the Distribution of the Traces of Frobenius

N. A. Carella

Let $E$ be a nonsingular elliptic curve over the rational numbers, and let $τ^{n} = p^{n} + 1 - # E (F_{p^{n}})$ . A result in the current literature claims that the normalized traces o…

math.GM2023

A Result for Germain Primes

N. A. Carella

This article determines a lower bound for the number Germain primes $p$ and $2 p + 1$ up to a large number $x$ .

math.GM2022

Equidistributions of Sign Patterns of the Liouville Function and Normal Numbers

N. A. Carella

The equidistribution of the double sign patterns of the Liouville function $λ$ is proved unconditionally. As application, it is shown that the computable real number $$\sum_{n \geq…

Note on the Exceptional Set in the ABC Conjecture

Small Prime kth Power Residues and Nonresidues in Arithmetic Progressions

Largest Prime Factors of Polynomials

Note on the Distribution of the Traces of Frobenius

A Result for Germain Primes

Equidistributions of Sign Patterns of the Liouville Function and Normal Numbers

Small Prime $k$ th Power Residues and Nonresidues in Arithmetic Progressions