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- Publisher Website: 10.1007/s00208-023-02713-8
- Scopus: eid_2-s2.0-85169579265
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Article: On length sets of subarithmetic hyperbolic manifolds
| Title | On length sets of subarithmetic hyperbolic manifolds |
|---|---|
| Authors | |
| Issue Date | 2-Sep-2023 |
| Publisher | Springer |
| Citation | Mathematische Annalen, 2023 How to Cite? |
| Abstract | In this paper, we study the set of lengths of closed geodesics (or equivalently, the set of traces of the fundamental group) of a hyperbolic manifold. By "subarithmetic," we mean a manifold whose set of traces takes values in a ring of algebraic integers. For such, we formulate the "Asymptotic Length-Saturation Conjecture", which states that, under certain natural conditions, there is an asymptotic local-global principle for the trace set. We prove the first instance of the conjecture for punctured, Zariski dense covers of the modular surface. |
| Persistent Identifier | http://hdl.handle.net/10722/338151 |
| ISSN | 2023 Impact Factor: 1.3 2023 SCImago Journal Rankings: 1.918 |
| ISI Accession Number ID |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Kontorovich, Alex | - |
| dc.contributor.author | Zhang, Xin | - |
| dc.date.accessioned | 2024-03-11T10:26:38Z | - |
| dc.date.available | 2024-03-11T10:26:38Z | - |
| dc.date.issued | 2023-09-02 | - |
| dc.identifier.citation | Mathematische Annalen, 2023 | - |
| dc.identifier.issn | 0025-5831 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/338151 | - |
| dc.description.abstract | <p>In this paper, we study the set of lengths of closed geodesics (or equivalently, the set of traces of the fundamental group) of a hyperbolic manifold. By "subarithmetic," we mean a manifold whose set of traces takes values in a ring of algebraic integers. For such, we formulate the "Asymptotic Length-Saturation Conjecture", which states that, under certain natural conditions, there is an asymptotic local-global principle for the trace set. We prove the first instance of the conjecture for punctured, Zariski dense covers of the modular surface.<br></p> | - |
| dc.language | eng | - |
| dc.publisher | Springer | - |
| dc.relation.ispartof | Mathematische Annalen | - |
| dc.title | On length sets of subarithmetic hyperbolic manifolds | - |
| dc.type | Article | - |
| dc.identifier.doi | 10.1007/s00208-023-02713-8 | - |
| dc.identifier.scopus | eid_2-s2.0-85169579265 | - |
| dc.identifier.eissn | 1432-1807 | - |
| dc.identifier.isi | WOS:001057075000001 | - |
| dc.identifier.issnl | 0025-5831 | - |