Arithmetic properties of representation zeta function

A representation zeta function (or Witten zeta function) is a Dirichlet series formed from the dimensions of irreducible representations of an algebraic object (e.g., of a Lie algebra, or Lie group). An example is the Riemann zeta function.

 

In this talk, we introduce some of the major properties of such zeta functions, discuss their special values and open conjectures, with an emphasis on the arithmetic side of the story.