تقرير
Equidistribution of high-rank polynomials with variables restricted to subsets of $\mathbb{F}_p$
| العنوان: | Equidistribution of high-rank polynomials with variables restricted to subsets of $\mathbb{F}_p$ |
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| المؤلفون: | Gowers, W. T., Karam, Thomas |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Mathematics - Number Theory, 11T06 (Primary) 11B30, 15A69 (Secondary) |
| الوصف: | Let $p$ be a prime and let $S$ be a non-empty subset of $\mathbb{F}_p$. Generalizing a result of Green and Tao on the equidistribution of high-rank polynomials over finite fields, we show that if $P: \mathbb{F}_p^n \rightarrow \mathbb{F}_p$ is a polynomial and its restriction to $S^n$ does not take each value with approximately the same frequency, then there exists a polynomial $P_0: \mathbb{F}_p^n \rightarrow \mathbb{F}_p$ that vanishes on $S^n$, such that the polynomial $P-P_0$ has bounded rank. Our argument uses two black boxes: that a tensor with high partition rank has high analytic rank and that a tensor with high essential partition rank has high disjoint partition rank. Comment: 42 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2209.04932 |
| رقم الأكسشن: | edsarx.2209.04932 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |