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arXiv · 1510.03721

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

Guillermo Matera·Mariana Perez·Melina Privitelli
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Abstract

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.

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Guillermo Matera, Mariana Perez, Melina Privitelli. 2015-10-13. Number of rational points of symmetric complete intersections over a finite field and applications. https://arxiv.org/abs/1510.03721

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