Linear Independence of Generalized Poincaré Series for Anti-de Sitter 3-Manifolds
Let Γ be a discrete group acting properly discontinuously and isometrically on the three-dimensional anti-de Sitter space AdS³, and □ the Laplacian, which is a second-order hyperbolic differential operator. We study the linear independence of a family of generalized Poincaré series introduced by Kas...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211307 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Linear Independence of Generalized Poincaré Series for Anti-de Sitter 3-Manifolds. Kazuki Kannaka. SIGMA 17 (2021), 042, 15 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Let Γ be a discrete group acting properly discontinuously and isometrically on the three-dimensional anti-de Sitter space AdS³, and □ the Laplacian, which is a second-order hyperbolic differential operator. We study the linear independence of a family of generalized Poincaré series introduced by Kassel-Kobayashi [Adv. Math. 287 (2016), 123-236, arXiv:1209.4075], which are defined by the Γ-average of certain eigenfunctions on AdS³. We prove that the multiplicities of 𝐿²-eigenvalues of the hyperbolic Laplacian □ on Γ∖AdS³ are unbounded when Γ is finitely generated. Moreover, we prove that the multiplicities of stable 𝐿²-eigenvalues for compact anti-de Sitter 3-manifolds are unbounded.
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| ISSN: | 1815-0659 |