## Illinois Journal of Mathematics

### Geometric zeta functions for higher rank $p$-adic groups

#### Abstract

The higher rank Lefschetz formula for $p$-adic groups is used to prove rationality of a several-variable zeta function attached to the action of a $p$-adic group on its Bruhat–Tits building. By specializing to certain lines one gets one-variable zeta functions, which then can be related to geometrically defined zeta functions.

#### Article information

Source
Illinois J. Math., Volume 58, Number 3 (2014), 719-738.

Dates
Received: 31 March 2014
Revised: 10 March 2015
First available in Project Euclid: 9 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1441790387

Digital Object Identifier
doi:10.1215/ijm/1441790387

Mathematical Reviews number (MathSciNet)
MR3395960

Zentralblatt MATH identifier
1377.11102

#### Citation

Deitmar, Anton; Kang, Ming-Hsuan. Geometric zeta functions for higher rank $p$-adic groups. Illinois J. Math. 58 (2014), no. 3, 719--738. doi:10.1215/ijm/1441790387. https://projecteuclid.org/euclid.ijm/1441790387

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