Computing local zeta functions of groups, algebras, and modules

Tobias Rossmann

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arXiv · 1602.00919

Computing local zeta functions of groups, algebras, and modules

Tobias Rossmann

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Abstract

We develop a practical method for computing local zeta functions of groups, algebras, and modules in fortunate cases. Using our method, we obtain a complete classification of generic local representation zeta functions associated with unipotent algebraic groups of dimension at most six. We also determine the generic local subalgebra zeta functions associated with $\mathfrak{gl}_2(\mathbf{Q})$. Finally, we introduce and compute examples of graded subobject zeta functions.

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Tobias Rossmann. 2016-02-02. Computing local zeta functions of groups, algebras, and modules. https://arxiv.org/abs/1602.00919

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