A note on lattice points in certain finite type domains in $\mathbb{R}^d$

TL;DR

This paper investigates the Fourier transforms of indicator functions for specific high-dimensional finite type domains and provides estimates for the discrepancy in counting lattice points within these domains.

Contribution

It introduces new estimates for lattice point discrepancies in certain finite type domains in high dimensions, advancing understanding in geometric number theory.

Findings

Derived bounds for lattice point discrepancy

Analyzed Fourier transforms of indicator functions

Extended results to high-dimensional finite type domains

Abstract

We study the Fourier transforms of indicator functions of some special high-dimensional finite type domains and obtain estimates of the associated lattice point discrepancy.