The Fundamental Theorem of prehomogeneous vector spaces modulo $p^m$. With an appendix "L-functions of prehomogeneous vector spaces" by Fumihiro Sato
| dc.creator | Cluckers, Raf | |
| dc.creator | Herremans, Adriaan | |
| dc.date | 2004-08-10 | |
| dc.date | 2005-08-03 | |
| dc.date.accessioned | 2026-07-07T05:11:11Z | |
| dc.date.available | 2026-07-07T05:11:11Z | |
| dc.description | 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 Fourier transform of a relative invariant of prehomogeneous vector spaces, where ${\mathcal P}$ is a big enough prime ideal of ${\mathcal O}_K$ and $m>1$. In the appendix, F. Sato gives an application of the Theorems A, B and the Theorems A, B, C in J. Denef and A. Gyoja [\emph{Character sums associated to prehomogeneous vector spaces}, Compos. Math., \textbf{113} (1998) 237--346] to the functional equation of $L$-functions of Dirichlet type associated with prehomogeneous vector spaces. | |
| dc.identifier | https://arxiv.org/abs/math/0408139 | |
| dc.identifier | http://arxiv.org/abs/math/0408139 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72157 | |
| dc.subject | Number Theory | |
| dc.subject | 11S90, 11L07, 11M41; 11T24, 11L05, 20G40 | |
| dc.title | The Fundamental Theorem of prehomogeneous vector spaces modulo $p^m$. With an appendix "L-functions of prehomogeneous vector spaces" by Fumihiro Sato | |
| dc.type | text |