Kida's formula for graphs with ramifications
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911965548380160 |
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| author | Kataoka, Takenori |
| author_facet | Kataoka, Takenori |
| contents | Recently Iwasawa theory for graphs is developing. A significant achievement includes an analogue of Iwasawa class number formula, which describes the asymptotic growth of the numbers of spanning trees for $\mathbb{Z}_p$-coverings of graphs. Moreover, an analogue of Kida's formula concerning the behavior of the $λ$- and $μ$-invariants is obtained for unramified coverings. In this paper, we establish Kida's formula for possibly ramified coverings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16934 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kida's formula for graphs with ramifications Kataoka, Takenori Combinatorics Number Theory 05C25, 11R23 Recently Iwasawa theory for graphs is developing. A significant achievement includes an analogue of Iwasawa class number formula, which describes the asymptotic growth of the numbers of spanning trees for $\mathbb{Z}_p$-coverings of graphs. Moreover, an analogue of Kida's formula concerning the behavior of the $λ$- and $μ$-invariants is obtained for unramified coverings. In this paper, we establish Kida's formula for possibly ramified coverings. |
| title | Kida's formula for graphs with ramifications |
| topic | Combinatorics Number Theory 05C25, 11R23 |
| url | https://arxiv.org/abs/2407.16934 |