On the error term of a lattice counting problem

TL;DR

This paper enhances the error bounds in lattice counting problems by applying advanced analytic techniques, including exponential sum bounds and Vaaler polynomials, building on recent research in the field.

Contribution

It introduces improved error estimates for lattice counting, utilizing novel analytic methods and bounds to refine previous results.

Findings

Enhanced error bounds for lattice counting problems.

Application of exponential sum bounds and Vaaler polynomials.

Improved estimates based on recent lattice counting research.

Abstract

We improve the error terms of some estimates related to counting lattices from recent work of L. Fukshansky, P. Guerzhoy and F. Luca (2017). This improvement is based on some analytic techniques, in particular on bounds of exponential sums coupled with the use of Vaaler polynomials.