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arXiv · 2301.09206

On some multiplicative properties of large difference sets

Ilya D. Shkredov
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Abstract

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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Ilya D. Shkredov. 2023-01-22. On some multiplicative properties of large difference sets. https://doi.org/10.4153/s0008414x23000500

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