Expanding phenomena over higher dimensional matrix rings
Combinatorics
2020-06-17 v2 Number Theory
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.
Cite
@article{arxiv.2006.08142,
title = {Expanding phenomena over higher dimensional matrix rings},
author = {Nguyen Van The and Le Anh Vinh},
journal= {arXiv preprint arXiv:2006.08142},
year = {2020}
}
Comments
Available Online in Journal of Number Theory, 21 pages