Zeta functions of three-dimensional p-adic Lie algebras
Zeta functions of three-dimensional p-adic Lie algebras
We give an explicit formula for the subalgebra zeta function of a general 3-dimensional Lie algebra over the p-adic integers. To this end, we associate to such a Lie algebra a ternary quadratic form over the p-adic integers. The formula for the zeta function is given in terms of Igusa’s local zeta function associated to this form.
subgroup growth, 3-dimensional Lie algebras, Igusa’s
local zeta function, ternary quadratic forms
195-210
Klopsch, Benjamin
3556ffc9-0748-4eee-aecc-d1dc70a30638
Voll, Christopher
b7bd2890-38ac-4e05-adb7-3b376916ff79
1 September 2009
Klopsch, Benjamin
3556ffc9-0748-4eee-aecc-d1dc70a30638
Voll, Christopher
b7bd2890-38ac-4e05-adb7-3b376916ff79
Klopsch, Benjamin and Voll, Christopher
(2009)
Zeta functions of three-dimensional p-adic Lie algebras.
Mathematische Zeitschrift, 263 (1), .
(doi:10.1007/s00209-008-0416-4).
Abstract
We give an explicit formula for the subalgebra zeta function of a general 3-dimensional Lie algebra over the p-adic integers. To this end, we associate to such a Lie algebra a ternary quadratic form over the p-adic integers. The formula for the zeta function is given in terms of Igusa’s local zeta function associated to this form.
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Submitted date: 10 October 2007
Published date: 1 September 2009
Keywords:
subgroup growth, 3-dimensional Lie algebras, Igusa’s
local zeta function, ternary quadratic forms
Organisations:
Pure Mathematics
Identifiers
Local EPrints ID: 56880
URI: http://eprints.soton.ac.uk/id/eprint/56880
ISSN: 0025-5874
PURE UUID: 943cd19a-20db-4128-b744-9e3cfd49e00f
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Date deposited: 12 Aug 2008
Last modified: 15 Mar 2024 11:04
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Contributors
Author:
Benjamin Klopsch
Author:
Christopher Voll
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