| Autor: |
Aichinger, Erhard, Grünbacher, Simon, Hametner, Paul |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
Finite Fields and Their Applications, Volume 95, 2024, 102379 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1016/j.ffa.2024.102379 |
| Popis: |
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 $S^N$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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