The balanced Voronoi formulas for GL(n)

TL;DR

This paper generalizes the GL(N) Voronoi summation formula to include hyper-Kloosterman sums, extending previous work on GL(4) and broadening the applicability of the formula in automorphic forms.

Contribution

It introduces a new formulation of the GL(N) Voronoi formula that incorporates hyper-Kloosterman sums, enhancing the analytical tools for automorphic forms on GL(n).

Findings

Generalizes the GL(N) Voronoi formula with hyper-Kloosterman sums

Extends previous GL(4) results to higher dimensions

Provides a unified framework for summation formulas in automorphic analysis

Abstract

In this paper we show how the GL(N) Voronoi summation formula of [MiSc2] can be rewritten to incorporate hyper-Kloosterman sums of various dimensions on both sides. This generalizes a formula for GL(4) with ordinary Kloosterman sums on both sides that was considered by Xiaoqing Li and the first-named author, and later by the second-named author in [Zho].