arXiv subjects

Marcelo Oliveira Veloso

Publications and source records attributed to Marcelo Oliveira Veloso.

3 recordsLinked to original sources

arXiv2025

On $\mathbb{F}_q$-primitive points on hypersurfaces

In this paper, we estimate the number of $\mathbb{F}_q$-primitive points on the affine hypersurface defined by the equation $f(x_1,\ldots,x_s)=0$, where $f\in\mathbb{F}_q[x_1,\dots,x_s]$ is an appropriate polynomial. In particular, we provide existence results for the case when $f$ is Dwork-regular and when $f$ is of Fermat type. Additionally, we present a proof for a recently posed conjecture. Finally, in the case where $q$ is a Fermat prime, we provide an explicit formula for the number of $\mathbb{F}_q$-primitive points on hyperplanes.

math.NT↗

arXiv2018

Rings of constants of linear derivations on Fermat rings

In this paper we characterize all the linear $\mathbb{C}$-derivations of the Fermat ring. We show that the Fermat ring has linear $\mathbb{C}$-derivations with trivial ring of constants and construct some examples.

math.AC↗

arXiv2015

Locally nilpotent derivations and automorphism groups of certain Danielewski surfaces

We describe the set of all locally nilpotent derivations of the quotient ring $\mathbb{K}[X,Y,Z]/(f(X)Y - φ(X,Z))$ constructed from the defining equation $f(X)Y = φ(X,Z)$ of a generalized Danielewski surface in $\mathbb K^3$ for a specific choice of polynomials $f$ and $φ$, with $\mathbb K$ an algebraically closed field of characteristic zero. As a consequence of this description we calculate the $ML$-invariant and the Derksen invariant of this ring. We also determine a set of generators for the group of $\mathbb K$-automorphisms of $\mathbb K[X,Y,Z]/(f(X)Y - φ(Z))$ also for a specific choice of polynomials $f$ and $φ$.

math.AC↗