On Weyl sums for smaller exponents

TL;DR

This paper introduces a hybrid method combining Vinogradov's mean value theorem to improve bounds on Weyl sums for intermediate exponents, advancing understanding in exponential sum estimates.

Contribution

It develops a new hybrid approach that enhances bounds on Weyl sums for smaller exponents, filling a gap in existing exponential sum estimates.

Findings

Derived new bounds for Weyl sums with intermediate exponents

Improved estimates using a hybrid approach with Vinogradov's mean value theorem

Applicable to a range of exponents, broadening previous results

Abstract

We present a hybrid approach to bounding exponential sums over kth powers via Vinogradov's mean value theorem, and derive estimates of utility for exponents k of intermediate size.