arXiv subjects

Mariana Perez

Publications and source records attributed to Mariana Perez.

2 recordsLinked to original sources

arXiv2020

Estimates on the number of rational solutions of variants of diagonal equations over finite fields

In this paper we study the set of rational solutions of equations defined by power sums symmetric polynomials with coefficients in a finite field. We do this by means of applying a methodology which relies on the study of the geometry of the set of common zeros of symmetric polynomials over the algebraic closure of a finite field. We provide improved estimates and existence results of rational solutions to the following equations: deformed diagonal equations, generalized Markoff Hurwitz type equations and Carlitz's equations. We extend these techniques to a more general variants of diagonal equations over finite fields.

math.NT↗

arXiv2015

Number of rational points of symmetric complete intersections over a finite field and applications

We study the set of common F_q-rational zeros of systems of multivariate symmetric polynomials with coefficients in a finite field F_q. We establish certain properties on these polynomials which imply that the corresponding set of zeros over the algebraic closure of F_q is a complete intersection with "good" behavior at infinity, whose singular locus has a codimension at least two or three. These results are used to estimate the number of F_q-rational points of the corresponding complete intersections. Finally, we illustrate the interest of these estimates through their application to certain classical combinatorial problems over finite fields.

math.NT↗