English

Expansion for the product of matrices in groups

Number Theory 2018-03-29 v2 Combinatorics

Abstract

In this paper, we give strong lower bounds on the size of the sets of products of matrices in some certain groups. More precisely, we prove an analogue of a result due to Chapman and Iosevich for matrices in SL2(Fp)SL_2(\mathbb{F}_p) with restricted entries on a small set. We also provide extensions of some recent results on expansion for cubes in Heisenberg group due to Hegyv\'{a}ri and Hennecart.

Keywords

Cite

@article{arxiv.1803.03351,
  title  = {Expansion for the product of matrices in groups},
  author = {Doowon Koh and Thang Pham and Chun-Yen Shen and Le Anh Vinh},
  journal= {arXiv preprint arXiv:1803.03351},
  year   = {2018}
}

Comments

v2: we have added some improvements