On some multiplicative properties of large difference sets

被引：0

作者：

Shkredov, Ilya D. ^{[1
]}

机构：

[1] London Inst Math Sci, 1 Albemarle St, London W1S 4BS, England

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2024年 / 76卷 / 05期

关键词：

Difference sets; sum-product; exponential sums; incidences; RESTRICTED SOLUTION SETS; FINITE-FIELDS; EQUATIONS; PRODUCT; THEOREM; EXPANSION;

D O I：

10.4153/S0008414X23000500

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1538 / 1555

页数：18

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