Clifford quartic forms and local functional equations of non-prehomogeneous type

TL;DR

This paper constructs degree-4 polynomials outside prehomogeneous vector spaces that still have associated local zeta functions satisfying functional equations, expanding understanding of non-prehomogeneous forms.

Contribution

It introduces new quartic polynomials not derived from prehomogeneous vector spaces with associated local zeta functions obeying functional equations.

Findings

Constructed degree-4 polynomials not from prehomogeneous vector spaces

Established local zeta functions satisfy functional equations for these polynomials

Extended the class of polynomials with known functional equations

Abstract

We construct polynomials of degree 4 that can not be obtained from prehomogeneous vector spaces, but, for which one can associate local zeta functions satisfying functional equations.