Translator Disclaimer
August 2018 Tree-Lattice Zeta Functions and Class Numbers
Anton Deitmar, Ming-Hsuan Kang
Michigan Math. J. 67(3): 617-645 (August 2018). DOI: 10.1307/mmj/1529460323

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.

Citation

Download Citation

Anton Deitmar. Ming-Hsuan Kang. "Tree-Lattice Zeta Functions and Class Numbers." Michigan Math. J. 67 (3) 617 - 645, August 2018. https://doi.org/10.1307/mmj/1529460323

Information

Received: 9 December 2016; Revised: 29 October 2017; Published: August 2018
First available in Project Euclid: 20 June 2018

zbMATH: 06969986
MathSciNet: MR3835566
Digital Object Identifier: 10.1307/mmj/1529460323

Subjects:
Primary: 20E08
Secondary: 11N05, 11N38, 11R29, 20F65, 22D05, 22E40, 57M07

Rights: Copyright © 2018 The University of Michigan

JOURNAL ARTICLE
29 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.67 • No. 3 • August 2018
Back to Top