Open Access
April, 2016 Zeta functions of ${\mathbb F}_1$-buildings
Anton DEITMAR, Ming-Hsuan KANG
J. Math. Soc. Japan 68(2): 807-822 (April, 2016). DOI: 10.2969/jmsj/06820807


The analogue of the Bruhat–Tits building of a $p$-adic group in F1-geometry is a single apartment. In this setting, the trace formula gives rise to a several variable zeta function analogously to the $p$-adic case. The analogy carries on to the fact that the restriction to certain lines yield zeta functions which are defined in geometrical terms. Also, the classical formula of Ihara has an analogue in this setting.


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Anton DEITMAR. Ming-Hsuan KANG. "Zeta functions of ${\mathbb F}_1$-buildings." J. Math. Soc. Japan 68 (2) 807 - 822, April, 2016.


Published: April, 2016
First available in Project Euclid: 15 April 2016

zbMATH: 1377.11062
MathSciNet: MR3488147
Digital Object Identifier: 10.2969/jmsj/06820807

Primary: 11F70
Secondary: 11F25 , 11F66 , 14G10 , 20E42

Keywords: Bruhat–Tits building , field of one element , Ihara zeta function

Rights: Copyright © 2016 Mathematical Society of Japan

Vol.68 • No. 2 • April, 2016
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