Image for the paper "On some multiplicative properties of large difference sets"
Image for the paper "On some multiplicative properties of large difference sets"
Image for the paper "On some multiplicative properties of large difference sets"
Image for the paper "On some multiplicative properties of large difference sets"
Image for the paper "On some multiplicative properties of large difference sets"
Image for the paper "On some multiplicative properties of large difference sets"
Image for the paper "On some multiplicative properties of large difference sets"
Image for the paper "On some multiplicative properties of large difference sets"
Image for the paper "On some multiplicative properties of large difference sets"
Image for the paper "On some multiplicative properties of large difference sets"
Image for the paper "On some multiplicative properties of large difference sets"
Image for the paper "On some multiplicative properties of large difference sets"
Image for the paper "On some multiplicative properties of large difference sets"
Image for the paper "On some multiplicative properties of large difference sets"
Image for the paper "On some multiplicative properties of large difference sets"
Image for the paper "On some multiplicative properties of large difference sets"

Multiplicativity of sets

Number theory

Expanding the known multiplicative properties of large difference sets yields a new, quantitative proof on the structure of product sets.

On some multiplicative properties of large difference sets

Canadian Journal of Mathematics, in press  (2023)

I. Shkredov

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

Canadian Journal of Mathematics, in press  (2023)

I. Shkredov