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• W2010935172 abstract "In this paper, we give a more direct proof of the results by Clair and Mokhtari-Sharghi [B. Clair, S. Mokhtari-Sharghi, Zeta functions of discrete groups acting on trees, J. Algebra 237 (2001) 591–620] on the zeta functions of periodic graphs. In particular, using appropriate operator-algebraic techniques, we establish a determinant formula in this context and examine its consequences for the Ihara zeta function. Moreover, we answer in the affirmative one of the questions raised in [R.I. Grigorchuk, A. Żuk, The Ihara zeta function of infinite graphs, the KNS spectral measure and integrable maps, in: V.A. Kaimanovich, et al. (Eds.), Proc. Workshop, Random Walks and Geometry, Vienna, 2001, de Gruyter, Berlin, 2004, pp. 141–180] by Grigorchuk and Żuk. Accordingly, we show that the zeta function of a periodic graph with an amenable group action is the limit of the zeta functions of a suitable sequence of finite subgraphs." @default.
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• W2010935172 date "2008-09-01" @default.
• W2010935172 modified "2023-09-24" @default.
• W2010935172 title "Ihara's zeta function for periodic graphs and its approximation in the amenable case" @default.
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• W2010935172 doi "https://doi.org/10.1016/j.jfa.2008.07.011" @default.
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