Resonances on geometrically finite graphs
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915895145660416 |
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| author | Arends, Christian Peterson, Carsten Weich, Tobias |
| author_facet | Arends, Christian Peterson, Carsten Weich, Tobias |
| contents | In analogy with the spectral theory of geometrically finite hyperbolic manifolds, we initiate the study of resonances on geometrically finite (q+1)-regular graphs of groups. We prove the meromorphic continuation of the resolvent of the adjacency operator on such spaces and give a geometric characterization of the resonant states. In contrast to the hyperbolic surfaces setting, geometrically finite graphs have only finitely many resonances and may be computed explicitly, yet exhibit many of the same qualitative phenomena as in the hyperbolic manifolds setting. Particularly interesting examples arise from algebraic curves over finite fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26443 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Resonances on geometrically finite graphs Arends, Christian Peterson, Carsten Weich, Tobias Spectral Theory Combinatorics Group Theory Number Theory 47A10, 05C50, 05C25, 58J50, 11G20 In analogy with the spectral theory of geometrically finite hyperbolic manifolds, we initiate the study of resonances on geometrically finite (q+1)-regular graphs of groups. We prove the meromorphic continuation of the resolvent of the adjacency operator on such spaces and give a geometric characterization of the resonant states. In contrast to the hyperbolic surfaces setting, geometrically finite graphs have only finitely many resonances and may be computed explicitly, yet exhibit many of the same qualitative phenomena as in the hyperbolic manifolds setting. Particularly interesting examples arise from algebraic curves over finite fields. |
| title | Resonances on geometrically finite graphs |
| topic | Spectral Theory Combinatorics Group Theory Number Theory 47A10, 05C50, 05C25, 58J50, 11G20 |
| url | https://arxiv.org/abs/2603.26443 |