Estimates for a three-dimensional exponential sum with monomials

TL;DR

This paper investigates three-dimensional exponential sums with monomials, offering improved estimates over existing bounds in certain cases, advancing understanding in this area of analytic number theory.

Contribution

It introduces sharper estimates for a class of three-dimensional exponential sums with monomials, surpassing previous bounds in specific scenarios.

Findings

New bounds for exponential sums with monomials

Enhanced estimates outperform existing approaches in some cases

Contributes to analytic number theory techniques

Abstract

We examine a family of three-dimensional exponential sums with monomials and provide estimates which are in some instances sharper than those stemming from approaches entailing the use of existing bounds pertaining to analogous sums.