Equivariant Poincar\'e series and monodromy zeta functions of quasihomogeneous polynomials

TL;DR

This paper develops an equivariant framework linking Poincaré series and monodromy zeta functions of quasihomogeneous polynomials using Burnside rings, extending previous non-equivariant relations.

Contribution

It introduces an equivariant version of the relation between Poincaré series and monodromy zeta functions utilizing Burnside rings of finite abelian groups.

Findings

Formulates an equivariant relation in terms of Burnside rings.

Extends classical relations to an equivariant setting.

Provides a new algebraic framework for analyzing quasihomogeneous polynomials.

Abstract

In earlier work, the authors described a relation between the Poincar\'e series and the classical monodromy zeta function corresponding to a quasihomogeneous polynomial. Here we formulate an equivariant version of this relation in terms of the Burnside rings of finite abelian groups and their analogues.