Zeta functions of 3-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 Zp. To this end, we associate to such a Lie algebra a ternary quadratic form over Zp. The formula for the zeta function is given in terms of Igusa's local zeta function associated to this form.

Keywords

Subgroup growth, 3-dimensional Lie algebras, Igusa's local zeta function, ternary quadratic forms

URI

https://doi.org/10.34657/3495
https://oa.tib.eu/renate/handle/123456789/1748

Citation

Klopsch, B., & Voll, C. (2007). Zeta functions of 3-dimensional p-Adic lie algebras (Vol. 2007-10). Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach. https://doi.org//10.14760/OWP-2007-10

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Mathematik

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