N. Carella

activity

20052026

most citedPrime Values of Quadratic Polynomials

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

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Showing 2021Show all

8 papers · 1 filter

math.GM2021

Prescribed Primitive Roots And The Least Primes

N. A. Carella

Let $q \neq = \pm 1, v^{2}$ be a fixed integer, and let $x \geq 1$ be a large number. The least prime number $p \geq 3$ such that $q$ is a primitive root modulo $p$ is conjectured to be $p\…

math.GM2021

Equidistribution Mod $1$ And Normal Numbers

N. A. Carella

Let $α = 0. a_{1} a_{2} a_{3} \dots$ be an irrational number in base $b > 1$ , where $0 \leq a_{i} < b$ . The number $α \in (0, 1)$ is a \textit{normal number} if every block $(a_{n+1}a_{n+2}\ldots a_{n…

math.GM2021

Sum of Divisors Function And The Largest Integer Function Over The Shifted Primes

N. A. Carella

Let $x \geq 1$ be a large number, let $[x] = x - {x}$ be the largest integer function, and let $σ (n)$ be the sum of divisors function. This note presents the first proof of the a…

math.GM2021

Euler Totient Function And The Largest Integer Function Over The Shifted Primes

N. A. Carella

Let $x \geq 1$ be a large number, let $[x] = x - {x}$ be the largest integer function, and let $φ (n)$ be the Euler totient function. The asymptotic formula for the new finite sum…

math.GM2021

Upper Bound of the Least Quadratic Nonresidues

N. A. Carella

Let $p \geq 3$ be a large prime and let $n (p) \geq 2$ denotes the least quadratic nonresidue modulo $p$ . This note sharpens the standard upper bound of the least quadratic nonresidue f…

math.GM2021

Approximate Atkin-Serre Conjecture

N. A. Carella

Let $λ (m)$ be the $m$ th coefficient of a modular form $f (z) = \sum_{m \geq 1} λ (m) q^{m}$ of weight $k \geq 4$ , let $p^{n}$ be a prime power, and let $ε > 0$ be a small number. An a…

Prescribed Primitive Roots And The Least Primes

Equidistribution Mod 1 And Normal Numbers

Sum of Divisors Function And The Largest Integer Function Over The Shifted Primes

Euler Totient Function And The Largest Integer Function Over The Shifted Primes

Upper Bound of the Least Quadratic Nonresidues

Approximate Atkin-Serre Conjecture

Equidistribution Mod $1$ And Normal Numbers