Applications of non-Archimedean integration to the $L$-series of $τ$-sheaves
| dc.creator | Goss, David | |
| dc.date | 2003-07-29 | |
| dc.date | 2004-05-04 | |
| dc.date.accessioned | 2026-07-07T04:59:57Z | |
| dc.date.available | 2026-07-07T04:59:57Z | |
| dc.description | Let $\underline{\mathcal F}$ be a $τ$-sheaf. Building on previous work of Drinfeld, Anderson, Taguchi, and Wan, Böckle and Pink \cite{bp1} develop a cohomology theory for $\underline{\mathcal F}$. In \cite{boc1} Böckle uses this theory to establish the analytic continuation of the $L$-series associated to $\underline{\mathcal F}$ (which is a characteristic $p$ valued ``Dirichlet series'') {\em and} the logarithmic growth of the degrees of its special polynomials. In this paper we shall show that this logarithmic growth is all that is needed to analytically continue the original $L$-series as well as {\em all} associated partial $L$-series. Moreover, we show that the degrees of the special polynomials attached to the partial $L$-series also grow logarithmically. Our tools are Böckle's original results, non-Archimedean integration, and the very strong estimates of Y. Amice \cite{am1}. Along the way, we define certain natural modules associated with non-Archimedean measures (in the characteristic 0 case as well as in characteristic $p$). | |
| dc.description | To appear in the Journal of Number Theory in the volume devoted to Arnold Ross | |
| dc.identifier | https://arxiv.org/abs/math/0307376 | |
| dc.identifier | http://arxiv.org/abs/math/0307376 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68198 | |
| dc.subject | Number Theory | |
| dc.subject | 11M38,11G09, 11F52 | |
| dc.title | Applications of non-Archimedean integration to the $L$-series of $τ$-sheaves | |
| dc.type | text |