Some questions on spectrum and arithmetic of locally symmetric spaces

TL;DR

This paper explores how the spectrum and arithmetic properties of locally symmetric spaces, defined by congruent arithmetical lattices, are interconnected, using automorphic representations as a framework.

Contribution

It formulates and investigates the relationship between spectrum and arithmetic in locally symmetric spaces within the context of automorphic representations.

Findings

Proposes a framework linking spectrum and arithmetic

Highlights the role of automorphic representations in this relationship

Raises questions for further research in the field

Abstract

We consider the question that the spectrum and arithmetic of locally symmetric spaces defined by congruent arithmetical lattices should mutually determine each other. We frame these questions in the context of automorphic representations.