# A Tauberian Approach to an Analog of Weyl's law for the Kohn Laplacian on Compact Heisenberg Manifolds

@inproceedings{Fan2021ATA, title={A Tauberian Approach to an Analog of Weyl's law for the Kohn Laplacian on Compact Heisenberg Manifolds}, author={Colin Fan and Elena Kim and Yunus E. Zeytuncu}, year={2021} }

Let M = Γ \ Hd be a compact quotient of the d-dimensional Heisenberg group Hd by a lattice subgroup Γ. We show that the eigenvalue counting function N(λ) for any fixed element of a family of second order differential operators {Lα} on M has asymptotic behavior N (λ) ∼ Cd,α vol (M)λ , where Cd,α is a constant that only depends on the dimension d and the parameter α. As a consequence, we obtain an analog of Weyl’s law (both on functions and forms) for the Kohn Laplacian on M . Our main tools are… Expand

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