Computing local zeta functions of groups, algebras, and modules

@article{Rossmann2016ComputingLZ,
  title={Computing local zeta functions of groups, algebras, and modules},
  author={T. Rossmann},
  journal={arXiv: Group Theory},
  year={2016}
}
  • T. Rossmann
  • Published 2 February 2016
  • Mathematics
  • arXiv: Group Theory
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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