A Voronoi summation formula for the shifted triple divisor function

TL;DR

This paper establishes a Voronoi summation formula for the shifted triple divisor function, utilizing the functional equation of the shifted $GL(3)$ Estermann function, advancing analytical techniques in number theory.

Contribution

It introduces a new Voronoi summation formula for the shifted 3-fold divisor function based on the functional equation of the shifted $GL(3)$ Estermann function.

Findings

Proves a Voronoi summation formula for the shifted 3-fold divisor function.

Provides the functional equation for the shifted $GL(3)$ Estermann function.

Enhances analytical tools for studying divisor functions and automorphic forms.

Abstract

In this paper, we prove a Voronoi summation formula for the shifted 3-fold divisor function twisted by additive characters. As the main tool, we provide the functional equation for the shifted $GL(3)$ Estermann function.