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 -norm of the direction set, and the -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