On Sums Involving Fourier Coefficients of Maass Forms for $\mathrm{SL}(3,\mathbb Z)$

TL;DR

This paper develops a truncated Voronoi identity for sums of Fourier coefficients of Maass forms on SL(3,Z), leading to new pointwise and second moment estimates for these sums.

Contribution

It introduces a truncated Voronoi formula for twisted sums of Fourier coefficients of SL(3,Z) Maass forms, providing new analytical tools.

Findings

Derived a truncated Voronoi identity for Fourier coefficient sums

Obtained pointwise estimates for these sums

Established second moment bounds

Abstract

We derive a truncated Voronoi identity for rationally additively twisted sums of Fourier coefficients of Maass forms for $\mathrm{SL}(3,\mathbb Z)$, and as an application obtain a pointwise estimate and a second moment estimate for the sums in question.