English

Group action and $L^2$-norm estimates of geometric problems

Combinatorics 2023-09-21 v2 Number Theory

Abstract

In 2017, by using the group theoretic approach, Bennett, Hart, Iosevich, Pakianathan, and Rudnev obtained a number of results on the distribution of simplices and sum-product type problems. The main purpose of this paper is to give a series of new applications of their powerful framework, namely, we focus on the product and quotient of distance sets, the L2L^2-norm of the direction set, and the L2L^2-norm of scales in difference sets.

Keywords

Cite

@article{arxiv.2208.04827,
  title  = {Group action and $L^2$-norm estimates of geometric problems},
  author = {Thang Pham},
  journal= {arXiv preprint arXiv:2208.04827},
  year   = {2023}
}

Comments

v2: accepted version