Lattice points in model domains of finite type in $\mathbb{R}^d$, II

TL;DR

This paper investigates the distribution of lattice points within certain high-dimensional finite type domains by analyzing the Fourier transforms of their indicator functions to understand their geometric and number-theoretic properties.

Contribution

It introduces new methods for estimating Fourier transforms of indicator functions for finite type domains in high dimensions, advancing lattice point counting techniques.

Findings

Derived bounds for Fourier transforms of indicator functions.

Improved estimates for lattice point counts in finite type domains.

Extended previous results to higher dimensions and more general domains.

Abstract

We study the lattice point problem associated with a special class of high-dimensional finite type domains via estimating the Fourier transforms of corresponding indicator functions.