Additive twists of Fourier coefficients of symmetric-square lifts

TL;DR

This paper investigates bounds on additively twisted Fourier coefficients of symmetric-square lifts of Maass forms, providing uniform estimates relative to spectral parameters and additive twists.

Contribution

It introduces new uniform bounds for these Fourier coefficients, advancing understanding of their behavior under additive twists.

Findings

Established bounds are uniform in spectral parameters.

Derived estimates are uniform in additive twists.

Results improve previous bounds on Fourier coefficients.

Abstract

We study the sum of additively twisted Fourier coefficients of a symmetric-square lift of a Maass form invariant under the full modular group. Our bounds are uniform in terms of the spectral parameter of the Maass form, as well as in terms of the additive twist.