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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Computing local zeta functions of groups, algebras, and modules


Author: Tobias Rossmann
Journal: Trans. Amer. Math. Soc. 370 (2018), 4841-4879
MSC (2010): Primary 11M41, 20F69, 20G30, 20F18, 20C15
DOI: https://doi.org/10.1090/tran/7361
Published electronically: December 27, 2017
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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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Additional Information

Tobias Rossmann
Affiliation: Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Germany
Address at time of publication: Department of Mathematics, University of Auckland, Auckland, New Zealand
Email: tobias.rossmann@gmail.com

DOI: https://doi.org/10.1090/tran/7361
Keywords: Subgroup growth, representation growth, zeta functions, unipotent groups, Lie algebras.
Received by editor(s): February 2, 2016
Received by editor(s) in revised form: September 29, 2016
Published electronically: December 27, 2017
Additional Notes: This work was supported by the DFG Priority Programme “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory” (SPP 1489).
Article copyright: © Copyright 2017 American Mathematical Society

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