A lower bound for the error term in Weyl's law for certain Heisenberg manifolds

TL;DR

This paper establishes a lower bound for the error term in Weyl's law specifically for the spectral counting function of certain high-dimensional Heisenberg manifolds, advancing understanding of spectral asymptotics.

Contribution

It provides an Omega-result that sets a fundamental lower limit on the error term in Weyl's law for these manifolds, which was previously not well-understood.

Findings

Established a lower bound for the error term in Weyl's law

Demonstrated the Omega-result for specific Heisenberg manifolds

Enhanced understanding of spectral asymptotics in geometric analysis

Abstract

This article provides an Omega-result for the remainder term in Weyl's law for the spectral counting function of certain (2l+1)-dimensional Heisenberg manifolds.