Third moment of the remainder term for Heisenberg manifolds
| dc.creator | Khosravi, Mahta | |
| dc.date | 2007-11-01 | |
| dc.date.accessioned | 2026-07-07T08:39:52Z | |
| dc.date.available | 2026-07-07T08:39:52Z | |
| dc.description | Let R(t) be the remainder term in Weyl's law for a 3-dimensional Riemannian Heisenberg manifold with a certain arithmetic metric. We prove a third moment result stating that \int_1^T R(t)^3 dt =d_3 T^(13/4)+O_δ(T^(45/14+δ)), where d_3 is a specific positive constant which can be evaluated explicitly. This proves the asymmetric behavior of R(t) about the t-axis. This result is consistent with the conjecture of Petridis and Toth stating that R(t)=O_δ(t^(3/4+δ)). Similar results hold for (2n+1)-dimensional Heisenberg manifolds with arithmetic metrics. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/0711.0073 | |
| dc.identifier | http://arxiv.org/abs/0711.0073 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141219 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Spectral Theory | |
| dc.title | Third moment of the remainder term for Heisenberg manifolds | |
| dc.type | text |