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arXiv · 1803.08357

Expanding phenomena over matrix rings

Yeşim Demiroğlu Karabulut·Doowon Koh·Thang Pham·Chun-Yen Shen·Le Anh Vinh
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Abstract

In this paper, we study expanding phenomena in the setting of matrix rings. More precisely, we will prove that If $A$ is a set of $M_2(\mathbb{F}_q)$ and $|A|\gg q^{7/2}$, then we have \[|A(A+A)|, ~|A+AA|\gg q^4.\] If $A$ is a set of $SL_2(\mathbb{F}_q)$ and $|A|\gg q^{5/2}$, then we have \[|A(A+A)|, ~|A+AA|\gg q^4.\] We also obtain similar results for the cases of $A(B+C)$ and $A+BC$, where $A, B, C$ are sets in $M_2(\mathbb{F}_q)$.

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Yeşim Demiroğlu Karabulut, Doowon Koh, Thang Pham, Chun-Yen Shen, Le Anh Vinh. 2018-03-22. Expanding phenomena over matrix rings. https://arxiv.org/abs/1803.08357

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