Edge zeta function and closed cycles in the standard non-uniform complex from $\operatorname{PGL}_3$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913583909044224 |
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| author | Hong, Soonki Kwon, Sanghoon |
| author_facet | Hong, Soonki Kwon, Sanghoon |
| contents | In this paper, we define the edge zeta function of weighted complex. We also present the formula for the edge zeta function of the standard non-uniform complex $\operatorname{PGL}(3,\mathbb{F}_q[t])\backslash\operatorname{PGL}(3,\mathbb{F}_q(\!(t^{-1})\!))/\operatorname{PGL}(3,\mathbb{F}_q[\![t^{-1}]\!])$, arising from the group $\operatorname{PGL}_3$, as a rational function. Applying trunction in a specific direction is one of the main ingredient. As a result, we obtain the exact formula for the number of closed cycles coming from geodesics in the building. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15489 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Edge zeta function and closed cycles in the standard non-uniform complex from $\operatorname{PGL}_3$ Hong, Soonki Kwon, Sanghoon Group Theory Combinatorics Dynamical Systems Geometric Topology Number Theory Representation Theory Primary 37E15, 20E42, Secondary 22E50, 20G25 In this paper, we define the edge zeta function of weighted complex. We also present the formula for the edge zeta function of the standard non-uniform complex $\operatorname{PGL}(3,\mathbb{F}_q[t])\backslash\operatorname{PGL}(3,\mathbb{F}_q(\!(t^{-1})\!))/\operatorname{PGL}(3,\mathbb{F}_q[\![t^{-1}]\!])$, arising from the group $\operatorname{PGL}_3$, as a rational function. Applying trunction in a specific direction is one of the main ingredient. As a result, we obtain the exact formula for the number of closed cycles coming from geodesics in the building. |
| title | Edge zeta function and closed cycles in the standard non-uniform complex from $\operatorname{PGL}_3$ |
| topic | Group Theory Combinatorics Dynamical Systems Geometric Topology Number Theory Representation Theory Primary 37E15, 20E42, Secondary 22E50, 20G25 |
| url | https://arxiv.org/abs/2411.15489 |