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

TL;DR

This paper establishes a lower bound for the error term in Weyl's law specifically for certain odd-dimensional Heisenberg manifolds, extending previous work on even dimensions.

Contribution

It provides a new lower bound estimate for the spectral counting function's error term in odd-dimensional Heisenberg manifolds, building on prior results for even dimensions.

Findings

Derived a lower bound for the error term in Weyl's law for odd-dimensional Heisenberg manifolds.

Extended previous results from even to odd dimensions.

Contributed to the understanding of spectral asymptotics in geometric analysis.

Abstract

This article is concerned with estimations from below for the remainder term in Weyl's law for the spectral counting function of certain rational (2l+1)-dimensional Heisenberg manifolds. Concentrating on the case of odd l, it continues the work done in part I which dealt with even l.