Reduced zeta functions of Lie algebras

TL;DR

This paper introduces reduced zeta functions for Lie algebras, derived from motivic zeta functions, and explores their properties, including multiplicativity and functional equations, especially for Lie algebras with well-behaved bases.

Contribution

It defines reduced zeta functions for Lie algebras and analyzes their properties, providing new tools for understanding their structure.

Findings

Reduced zeta functions can be derived from motivic zeta functions using Euler characteristic.

Reduced zeta functions are multiplicative under certain conditions.

Some reduced zeta functions satisfy functional equations.

Abstract

We define reduced zeta functions of Lie algebras, which can be derived from motivic zeta functions using the Euler characteristic. We show that reduced zeta functions of Lie algebras possessing a suitably well-behaved basis are easy to analyse. We prove that reduced zeta functions are multiplicative under certain conditions and investigate which reduced zeta functions have functional equations.