Zeta functions of 3-dimensional p-adic Lie algebras

Details Zeta functions of 3-dimensional p-adic Lie algebras Zeta functions of 3-dimensional p-adic Lie algebras

2007-10-10

arxiv.org/abs/0710.1970v1

Mathematics

Group Theory

20 pages

Scientific paper

We give an explicit formula for the subalgebra zeta function of a general
3-dimensional Lie algebra over the p-adic integers $\mathbb{Z}_p$. To this end,
we associate to such a Lie algebra a ternary quadratic form over
$\mathbb{Z}_p$. The formula for the zeta function is given in terms of Igusa's
local zeta function associated to this form.

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