An improvement on the upper bound of exponential sums connected to holomorphic cusp forms

TL;DR

This paper enhances the upper bounds for short exponential sums related to holomorphic cusp forms, extending the range where these bounds are sharp and improving the understanding of their behavior.

Contribution

It provides a tighter upper bound for exponential sums connected to holomorphic cusp forms and broadens the range of sums for which the bounds are valid.

Findings

Improved upper bound for short exponential sums

Extended the range of sharp bounds

Enhanced understanding of exponential sums in number theory

Abstract

We improve the known upper bound for short exponential sums and increase the range on which a sharp upper bound is known.