Arithmetic harmonic analysis for smooth quartic Weyl sums: three additive equations

TL;DR

This paper proves the non-singular Hasse principle for systems of three diagonal quartic equations with at least 32 variables, using advanced harmonic analysis techniques and new moment estimates for smooth quartic Weyl sums.

Contribution

It introduces novel harmonic analysis methods and a new tenth moment estimate for smooth quartic Weyl sums to establish the Hasse principle for these systems.

Findings

Proves the non-singular Hasse principle for three diagonal quartic systems in 32+ variables.

Develops a new estimate for the tenth moment of smooth quartic Weyl sums.

Employs arithmetic harmonic analysis techniques in this context.

Abstract

We establish the non-singular Hasse principle for systems of three diagonal quartic equations in 32 or more variables, subject to a certain rank condition. Our methods employ the arithmetic harmonic analysis of smooth quartic Weyl sums and also a new estimate for their tenth moment.