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arXiv · 2407.16934

Kida's formula for graphs with ramifications

Takenori Kataoka
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Abstract

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.

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Takenori Kataoka. 2024-07-24. Kida's formula for graphs with ramifications. https://arxiv.org/abs/2407.16934

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