Zeta functions of 3-dimensional p-adic Lie algebras

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Date
2007-03-26MFO Scientific Program
Research in Pairs 2007Series
Oberwolfach Preprints;2007,10Author
Klopsch, Benjamin
Voll, Christopher
Metadata
Show full item recordOWP-2007-10
Abstract
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.