Group action and L2-norm estimates of geometric problems

In 2017, by using the group theoretic approach and tools from discrete Fourier analysis, 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 L2 norm of the direction set, and the L2-norm of scales in difference sets.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This paper presents new applications of the powerful framework developed by Bennett, Hart, Iosevich, Pakianathan, and Rudnev, which involve the product and quotient of distance sets, the L2 norm of the direction set, and the L2-norm of scales in difference sets.