Additive twists of Fourier coefficients of GL(3) Maass forms

TL;DR

This paper proves that sums of Fourier coefficients of GL(3) Maass forms, twisted by additive characters, exhibit cancellation uniformly across different forms, advancing understanding of their oscillatory behavior.

Contribution

It establishes uniform cancellation results for additive twists of Fourier coefficients of GL(3) Maass forms, a novel advancement in the analytic theory of automorphic forms.

Findings

Proves cancellation in sums of Fourier coefficients with additive twists.

Results hold uniformly across different GL(3) Maass forms.

Enhances understanding of oscillatory behavior of Fourier coefficients.

Abstract

We prove cancellation in a sum of Fourier coefficents of a GL(3) form $F$ twisted by additive characters, uniformly in the form $F$.