S. Ribas

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20232026

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math.NT2026

Arithmetic properties of arguments of algebraic numbers on the unit circle

Geraldo César Gonçalves Ferreira, Sávio Ribas

An irrational number $θ$ is called Diophantine if there exist $c > 0$ and $τ < \infty$ such that $θ - \frac{p}{q} \geq \frac{c}{q ^{τ}}$ holds for every $(p,q) \in \mathbb{Z…

math.NT2025

Some zero-sum problems over $⟨ x, y ∣ x^{2} = y^{n /2}, y^{n} = 1, y x = x y^{s} ⟩$

Sávio Ribas

Let $n \geq 8$ be even, and let $G = ⟨ x, y ∣ x^{2} = y^{n /2}, y^{n} = 1, y x = x y^{s} ⟩$ , where $s^{2} \equiv 1 (mod n)$ and $s \neq \equiv \pm 1 (mod n)$ . In this paper, we pr…

math.NT2024

A note on weighted consecutive Davenport constant

A. Lemos, A. O. Moura, S. Ribas +1

Let $G$ be a group and $A \subseteq [1, exp (G) - 1]$ . We define the constant $C_{A} (G),$ which is the least positive integer $ℓ$ such that every sequence over $G$ of length at…

math.NT2023

A note on Bass' conjecture

Danilo Vilela Avelar, Fabio Enrique Brochero Martínez, Sávio Ribas

For a finite group $G$ , we denote by $d (G)$ and by $E (G)$ , respectively, the small Davenport constant and the Gao constant of $G$ . Let $C_{n}$ be the cyclic group of orde…

Arithmetic properties of arguments of algebraic numbers on the unit circle

Some zero-sum problems over ⟨x,y∣x2=yn/2,yn=1,yx=xys⟩

A note on weighted consecutive Davenport constant

A note on Bass' conjecture

Some zero-sum problems over $⟨ x, y ∣ x^{2} = y^{n /2}, y^{n} = 1, y x = x y^{s} ⟩$