Square values of several polynomials over a finite field

2024/07/15 by Slavov, Kaloyan · 2 citations
#11T06 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14G15 #Secondary 14G05

paper · doi:10.48550/arxiv.2407.10538

Abstract

Let f₁,…,f_m be polynomials in n variables with coefficients in a finite field \mathbbF_q. We estimate the number of points \underlinex in \mathbbF_qⁿ such that each value f_i(\underlinex) is a nonzero square in \mathbbF_q. The error term is especially small when the f_i 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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