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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.19669 |
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Table of Contents:
- We consider sparse polynomials in $N$ variables over a finite field, and ask whether they vanish on a set $S^N$, where $S$ is a set of nonzero elements of the field. We see that if for a polynomial $f$, there is $\mathbf{c}\in S^N$ with $f (\mathbf{c}) \neq 0$, then there is such a $\mathbf{c}$ in every sphere inside $S^N$, where the radius of the sphere is bounded by a multiple of the logarithm of the number of monomials that appear in $f$. A similar result holds for the solutions of the equations $f_1 = \cdots = f_r = 0$ inside $S^N$.