July 15, 2024Open Access

Square values of several polynomials over a finite field

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Abstract

Let f₁, , fₘ be polynomials in n variables with coefficients in a finite field Fq. We estimate the number of points x in Fqⁿ such that each value fᵢ (x) is a nonzero square in Fq. The error term is especially small when the fᵢ define smooth projective quadrics with nonsingular intersections. We improve the error term in a recent work by Asgarli--Yip on mutual position of smooth quadrics.

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Cite This Study

Kaloyan Slavov (Mon,) studied this question.

synapsesocial.com/papers/68e60550b6db643587598949 https://doi.org/https://doi.org/10.48550/arxiv.2407.10538

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