Illinois Journal of Mathematics

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

Anton Deitmar and Ming-Hsuan Kang

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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

Subjects
Primary: 11M41: Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields 11F72: Spectral theory; Selberg trace formula 11F75: Cohomology of arithmetic groups 20E42: Groups with a $BN$-pair; buildings [See also 51E24] 51E24: Buildings and the geometry of diagrams

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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