Higher order invariants in the case of compact quotients

TL;DR

This paper develops a theory of higher order invariants and automorphic forms specifically for compact quotients, simplifying the general case and enabling a more detailed structure theorem.

Contribution

It introduces a simplified framework for higher order invariants in compact quotients and proves a more precise structure theorem than in the general case.

Findings

Simplified theory of higher order invariants for compact quotients

Proved a more precise structure theorem in this setting

Enhanced understanding of automorphic forms in compact cases

Abstract

We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case many things simplify and we are thus able to prove a more precise structure theorem than in the general case.