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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2021 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | 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 |
| Цитувати: | Linear Independence of Generalized Poincaré Series for Anti-de Sitter 3-Manifolds. Kazuki Kannaka. SIGMA 17 (2021), 042, 15 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862621759859064832 |
|---|---|
| author | Kannaka, Kazuki |
| author_facet | Kannaka, Kazuki |
| citation_txt | Linear Independence of Generalized Poincaré Series for Anti-de Sitter 3-Manifolds. Kazuki Kannaka. SIGMA 17 (2021), 042, 15 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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 ²-eigenvalues of the hyperbolic Laplacian □ on Γ∖AdS³ are unbounded when Γ is finitely generated. Moreover, we prove that the multiplicities of stable ²-eigenvalues for compact anti-de Sitter 3-manifolds are unbounded.
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| first_indexed | 2026-03-14T13:22:12Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211307 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T13:22:12Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kannaka, Kazuki 2025-12-29T11:07:58Z 2021 Linear Independence of Generalized Poincaré Series for Anti-de Sitter 3-Manifolds. Kazuki Kannaka. SIGMA 17 (2021), 042, 15 pages 1815-0659 2020 Mathematics Subject Classification: 58J50; 53C50; 22E40 arXiv:2005.03308 https://nasplib.isofts.kiev.ua/handle/123456789/211307 https://doi.org/10.3842/SIGMA.2021.042 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 ²-eigenvalues of the hyperbolic Laplacian □ on Γ∖AdS³ are unbounded when Γ is finitely generated. Moreover, we prove that the multiplicities of stable ²-eigenvalues for compact anti-de Sitter 3-manifolds are unbounded. The author would like to express his sincere gratitude to Professor Toshiyuki Kobayashi, whose suggestions led him to study the multiplicities of ²-eigenvalues for anti-de Sitter manifolds. He also would like to show his appreciation to Dr. Hiroyoshi Tamori, whose comments led him to an explicit description of (, , ε, s) in Lemma 3.3. Thanks are also due to the anonymous referees for their helpful comments to improve the paper. This work was supported by JSPS KAKENHI Grant Number 18J20157 and the Program for Leading Graduate Schools, MEXT, Japan. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Linear Independence of Generalized Poincaré Series for Anti-de Sitter 3-Manifolds Article published earlier |
| spellingShingle | Linear Independence of Generalized Poincaré Series for Anti-de Sitter 3-Manifolds Kannaka, Kazuki |
| title | Linear Independence of Generalized Poincaré Series for Anti-de Sitter 3-Manifolds |
| title_full | Linear Independence of Generalized Poincaré Series for Anti-de Sitter 3-Manifolds |
| title_fullStr | Linear Independence of Generalized Poincaré Series for Anti-de Sitter 3-Manifolds |
| title_full_unstemmed | Linear Independence of Generalized Poincaré Series for Anti-de Sitter 3-Manifolds |
| title_short | Linear Independence of Generalized Poincaré Series for Anti-de Sitter 3-Manifolds |
| title_sort | linear independence of generalized poincaré series for anti-de sitter 3-manifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211307 |
| work_keys_str_mv | AT kannakakazuki linearindependenceofgeneralizedpoincareseriesforantidesitter3manifolds |