Zeta functions of quasi-split reductive algebraic groups over local fields

We calculate zeta functions of quasi-split reductive algebraic groups over local fields using the classification of Tits and prove a functional equation. We give explicit exam- ples of these zeta functions for non-split unitary and orthogonal groups.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-11-02
DOI
https://doi.org/10.48550/arxiv.2611.03470
Primary Topic
Advanced Algebra and Geometry
Type
preprint
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preprint

Zeta functions of quasi-split reductive algebraic groups over local fields

Marcus Du Sautoy
arXiv (Cornell University)
Advanced Algebra and Geometry
preprint

Zeta functions of quasi-split reductive algebraic groups over local fields

Marcus Du Sautoy
preprint en

Abstract

We calculate zeta functions of quasi-split reductive algebraic groups over local fields using the classification of Tits and prove a functional equation. We give explicit exam- ples of these zeta functions for non-split unitary and orthogonal groups.

arXiv (Cornell University)
Advanced Algebra and Geometry
DOIOpen Access PDFOpenAlex
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Zeta functions of quasi-split reductive algebraic groups over local fields — Marcus Du Sautoy · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS