A method for computing general automorphic forms on general groups

TL;DR

This paper introduces a general numerical method for computing automorphic forms on various groups using Voronoi-type summation formulas, demonstrated through a successful example on GL(3).

Contribution

It presents a novel, general computational approach for automorphic forms applicable to a wide range of groups, expanding computational techniques in the field.

Findings

Successfully computed a known cusp form on GL(3) using the method

Demonstrated the efficiency of the approach with a numerical example

Validated the method's potential for broader applications in automorphic form computation

Abstract

This article describes a general method for computing automorphic forms using Voronoi-type summation formulas. It gives a numerical example where the technique is successful in quickly finding a cusp form on GL(3,Z)\GL(3,R), albeit one whose existence was already known as a Langlands lift.