ID: 2301.09206

On some multiplicative properties of large difference sets

January 22, 2023

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Ilya D. Shkredov
Mathematics
Number Theory
Combinatorics

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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