Zeta functions of groups and rings - recent developments

TL;DR

This paper surveys recent advances in the study of zeta functions related to infinite groups and rings, focusing on counting subgroups, subrings, and representations of finite index or dimension.

Contribution

It provides a comprehensive overview of recent progress in understanding zeta functions associated with groups and rings, highlighting new theoretical developments.

Findings

New formulas for subgroup zeta functions

Recent classification results for zeta functions of rings

Connections between zeta functions and representation theory

Abstract

I survey some recent developments in the theory of zeta functions associated to infinite groups and rings, specifically zeta functions enumerating subgroups and subrings of finite index or finite-dimensional complex representations.