Homogeneity of arithmetic quantum limits for hyperbolic $4$-manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910397023387648 |
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| author | Shem-Tov, Zvi Silberman, Lior |
| author_facet | Shem-Tov, Zvi Silberman, Lior |
| contents | We work toward the arithmetic quantum unique ergodicity (AQUE) conjecture for sequences of Hecke--Maass forms on hyperbolic $4$-manifolds. We show that limits of such forms can only scar on totally geodesic $3$-submanifolds, and in fact that all ergodic components of the microlocal lift other than the uniform measure arise from the uniform measures on these submanifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18218 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homogeneity of arithmetic quantum limits for hyperbolic $4$-manifolds Shem-Tov, Zvi Silberman, Lior Number Theory Mathematical Physics Dynamical Systems 11F41, 37A45 We work toward the arithmetic quantum unique ergodicity (AQUE) conjecture for sequences of Hecke--Maass forms on hyperbolic $4$-manifolds. We show that limits of such forms can only scar on totally geodesic $3$-submanifolds, and in fact that all ergodic components of the microlocal lift other than the uniform measure arise from the uniform measures on these submanifolds. |
| title | Homogeneity of arithmetic quantum limits for hyperbolic $4$-manifolds |
| topic | Number Theory Mathematical Physics Dynamical Systems 11F41, 37A45 |
| url | https://arxiv.org/abs/2402.18218 |