On the error term in Weyl's law for the Heisenberg manifolds (II)

TL;DR

This paper investigates the average size of the error term in Weyl's law for high-dimensional irrational Heisenberg manifolds, establishing an asymptotic formula to better understand spectral counting errors.

Contribution

It provides a new asymptotic formula for the mean square of the error term in Weyl's law for irrational Heisenberg manifolds, advancing spectral geometry understanding.

Findings

Established an asymptotic formula for the mean square of the error term.

Enhanced understanding of spectral counting errors in high-dimensional manifolds.

Contributed to the spectral theory of Heisenberg manifolds.

Abstract

In this paper we study the mean square of the error term in the Weyl's law of an irrational $(2l+1)$-dimensional Heisenberg manifold . An asymptotic formula is established.