Square values of several polynomials over a finite field
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917722197065728 |
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| author | Slavov, Kaloyan |
| author_facet | Slavov, Kaloyan |
| contents | Let $f_1,\dots,f_m$ be polynomials in $n$ variables with coefficients in a finite field $\mathbb{F}_q$. We estimate the number of points $\underline{x}$ in $\mathbb{F}_q^n$ such that each value $f_i(\underline{x})$ is a nonzero square in $\mathbb{F}_q$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10538 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Square values of several polynomials over a finite field Slavov, Kaloyan Algebraic Geometry Primary 14G15, 11T06, Secondary 14G05 Let $f_1,\dots,f_m$ be polynomials in $n$ variables with coefficients in a finite field $\mathbb{F}_q$. We estimate the number of points $\underline{x}$ in $\mathbb{F}_q^n$ such that each value $f_i(\underline{x})$ is a nonzero square in $\mathbb{F}_q$. 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. |
| title | Square values of several polynomials over a finite field |
| topic | Algebraic Geometry Primary 14G15, 11T06, Secondary 14G05 |
| url | https://arxiv.org/abs/2407.10538 |