Kida’s formula for graphs with ramifications

Recently Iwasawa theory for graphs is being developed. A significant achievement includes an analogue of Iwasawa’s 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 $\lambda $- and $\mu $-invariants is obtained for unramified coverings. In this paper, we establish Kida’s formula for possibly ramified coverings.

Published in Open Access (under CC-BY license).