Title: Tree-Lattice Zeta Functions and Class Numbers
Authors: Deitmar, Anton
Kang, Ming-Hsuan
應用數學系
Department of Applied Mathematics
Issue Date: 1-Jan-2018
Abstract: We extend the theory of Ihara zeta functions to noncompact arithmetic quotients of Bruhat-Tits trees. This new zeta function turns out to be a rational function despite the infinite-dimensional setting. In general, it has zeros and poles in contrast to the compact case. The determinant formulas of Bass and Ihara hold if we define the determinant as the limit of all finite principal minors. From this analysis we derive a prime geodesic theorem, which, applied to special arithmetic groups, yields new asymptotic assertions on class numbers of orders in global fields.
URI: http://dx.doi.org/10.1307/mmj/1529460323
http://hdl.handle.net/11536/148228
ISSN: 0026-2285
DOI: 10.1307/mmj/1529460323
Journal: MICHIGAN MATHEMATICAL JOURNAL
Volume: 67
Begin Page: 617
End Page: 645
Appears in Collections:Articles