A general simple relative trace formula and a relative Weyl law

TL;DR

This paper introduces a broad, simplified relative trace formula and demonstrates its application by establishing a relative Weyl law, advancing the understanding of spectral distributions in a relative setting.

Contribution

It presents a new, general simple relative trace formula and applies it to prove a relative Weyl law, extending classical spectral analysis results.

Findings

Established a general simple relative trace formula.

Proved a relative analogue of the Weyl law.

Enhanced tools for spectral analysis in relative contexts.

Abstract

In this paper, we prove a general simple relative trace formula. As an application, we prove a relative analogue of the Weyl law.