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arXiv · 1912.05639

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

Mariana Perez·Melina Privitelli
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Abstract

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.

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Mariana Perez, Melina Privitelli. 2020-02-03. Estimates on the number of rational solutions of variants of diagonal equations over finite fields. https://arxiv.org/abs/1912.05639

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