Expanding phenomena over matrix rings
| Autor: | Karabulut, Yeşim Demiroğlu, Koh, Doowon, Pham, Thang, Shen, Chun-Yen, Vinh, Le Anh |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $M_2(\mathbb{F}_q)$. Comment: 31 pages |
| Databáze: | arXiv |
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