Computing local zeta functions of groups, algebras, and modules

2016/02/02 by Rossmann, Tobias
#11M41 #20C15 #20F18 #20F69 #20G30 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1602.00919

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 \mathfrakgl₂(Q). Finally, we introduce and compute examples of graded subobject zeta functions.

Related

• Functional equations for zeta functions of groups and rings
• Computing topological zeta functions of groups, algebras, and modules, II
• Topological representation zeta functions of unipotent groups
• Zeta functions of groups and rings - recent developments
• Uniformity and Functional Equations for Local Zeta Functions of \mathfrakK-Split Algebraic Groups