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

DOI10.1016/J.JMAA.2023.127748arXiv2208.04827OpenAlexW4386573414MaRDI QIDQ6407411

Thang V. Pham

Publication date: 9 August 2022

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 $L^2$-norm of the direction set, and the $L^2$-norm of scales in difference sets.

Full work available at URL: https://doi.org/10.1016/j.jmaa.2023.127748

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Erd?s problems and related topics of discrete geometry (52C10) Classical measure theory (28A99) Arithmetic combinatorics; higher degree uniformity (11B30)

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