The Fundamental Theorem of prehomogeneous vector spaces modulo $p^m$. With an appendix "L-functions of prehomogeneous vector spaces" by Fumihiro Sato

Raf Cluckers, Adriaan Herremans

For a number field $K$ with ring of integers ${\mathcal{O}}_K$, we prove an analogue over finite rings of the form ${\mathcal{O}}_K/{\mathcal{P}}^m$ of the Fundamental Theorem on the…