Asymptotics and zeta functions on compact nilmanifolds. (English) Zbl 1485.58023
The author obtains asymptotic formulae on nilmanifolds \(\Gamma\setminus G\) where \(G\) is any stratified nilpotent Lie group equipped with a co-compact discrete subgroup \(\Gamma\). He also studies the asymptotics related to the sub-Laplacians naturally coming from the stratified structure of the group \(G\). The author shows that the short-time asymptotic on the diagonal of the kernels of spectral multipliers contains only a single non-trivial term. The author also studies the associated zeta functions.
Reviewer: Shu-Yu Hsu (Chiayi)
MSC:
| 58J50 | Spectral problems; spectral geometry; scattering theory on manifolds |
| 58J35 | Heat and other parabolic equation methods for PDEs on manifolds |
| 35K08 | Heat kernel |
| 35P05 | General topics in linear spectral theory for PDEs |
| 53C17 | Sub-Riemannian geometry |
| 43A85 | Harmonic analysis on homogeneous spaces |
Keywords:
hypoelliptic operators; harmonic analysis on homogeneous spaces; global analysis and spectral problems; heat kernels; spectral multipliersReferences:
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