关于大差分集的若干乘法性质

Pub Date : 2023-01-22 DOI:10.4153/s0008414x23000500

I. Shkredov

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引用次数: 2

摘要

在合数$q$的情况下，研究了大集合$A \subseteq \mathbb{Z}/q\mathbb{Z}$的差分集$A-A$的乘法性质。我们得到了a . Fish关于积集$(a - a)$ (a - a)$结构的结果的一个定量版本。并且证明了任意差分集的乘法覆盖数总是很小的。

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On some multiplicative properties of large difference sets

In our paper we study multiplicative properties of difference sets $A-A$ for large sets $A \subseteq \mathbb{Z}/q\mathbb{Z}$ in the case of composite $q$. We obtain a quantitative version of a result of A. Fish about the structure of the product sets $(A-A)(A-A)$. Also, we show that the multiplicative covering number of any difference set is always small.

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