Expanding phenomena over higher dimensional matrix rings
arXiv:2006.08142 · doi:10.1016/j.jnt.2020.02.011
Abstract
In this paper, we study the expanding phenomena in the setting of higher dimensional matrix rings. More precisely, we obtain a sum-product estimate for large subsets and show that x+yz, x(y+z) are moderate expanders over the matrix ring, and xy + z + t is strong expander over the matrix rings. These results generalize recent results of Y.D. Karabulut, D. Koh, T. Pham, C-Y. Shen, and the second listed author.
Available Online in Journal of Number Theory, 21 pages