arXiv subjects

Luan Alberto Ferreira

Publications and source records attributed to Luan Alberto Ferreira.

4 recordsLinked to original sources

arXiv2026

Real exponential sums over primes and prime gaps

We prove that given $λ\in \mathbb{R}$ such that $0 < λ< 1$, then $π(x + x^λ) - π(x) \sim \displaystyle \frac{x^λ}{\log(x)}$. This solves a long-standing problem concerning the existence of primes in short intervals. In particular, we give a positive answer (for all sufficiently large number) to some old conjectures about prime numbers, such as Legendre's conjecture about the existence of at least two primes between two consecutive squares.

math.NT↗

arXiv2023

The triangular numbers are finitely stable

This small note proves that the set of triangular numbers is a finitely stable additive basis. This, together with a previous result by the author, shows that triangular numbers and squares are, among all polygonal numbers, the only ones that are finitely stable additive bases.

math.NT↗

arXiv2017

Some consequences of the Firoozbakht's conjecture

In this paper we present the statement of the Firoozbakht's conjecture, some of its consequences if it is proved and we show a consequence of Zhang's theorem concerning the Firoozbakht's conjecture.

math.NT↗

arXiv2014

A metric for the set of all additive basis

The aim of this article is to present a topological tool for the study of additive basis in additive number theory. It will be proposal a metric for the set of all additive basis, in which it will be possible to study properties of some additive bases studying basis near the chosen basis. This metric allow, for example, detect some additive basis in which we can add some integers in it without change its order.

math.NT↗