关于大差分集的若干乘法性质

IF 0.6 3区数学 Q3 MATHEMATICS

Canadian Journal of Mathematics-Journal Canadien De Mathematiques 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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来源期刊

Canadian Journal of Mathematics-Journal Canadien De Mathematiques 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4.5 months

期刊介绍： The Canadian Journal of Mathematics (CJM) publishes original, high-quality research papers in all branches of mathematics. The Journal is a flagship publication of the Canadian Mathematical Society and has been published continuously since 1949. New research papers are published continuously online and collated into print issues six times each year. To be submitted to the Journal, papers should be at least 18 pages long and may be written in English or in French. Shorter papers should be submitted to the Canadian Mathematical Bulletin. Le Journal canadien de mathématiques (JCM) publie des articles de recherche innovants de grande qualité dans toutes les branches des mathématiques. Publication phare de la Société mathématique du Canada, il est publié en continu depuis 1949. En ligne, la revue propose constamment de nouveaux articles de recherche, puis les réunit dans des numéros imprimés six fois par année. Les textes présentés au JCM doivent compter au moins 18 pages et être rédigés en anglais ou en français. C’est le Bulletin canadien de mathématiques qui reçoit les articles plus courts.