Hyperdifferential properties of Drinfeld quasi-modular forms
| dc.creator | Bosser, Vincent | |
| dc.creator | Pellarin, Federico | |
| dc.date | 2007-03-28 | |
| dc.date.accessioned | 2026-07-07T07:54:15Z | |
| dc.date.available | 2026-07-07T07:54:15Z | |
| dc.description | This article is divided in two parts. In the first part we endow a certain ring of ``Drinfeld quasi-modular forms'' for $\GL_2(\FF_q[T])$ (where $q$ is a power of a prime) with a system of "divided derivatives" (or hyperderivations). This ring contains Drinfeld modular forms as defined by Gekeler in \cite{Ge}, and the hyperdifferential ring obtained should be considered as a close analogue in positive characteristic of famous Ramanujan's differential system relating to the first derivatives of the classical Eisenstein series of weights 2, 4 and 6. In the second part of this article we prove that, when $q\not=2,3$, if ${\cal P}$ is a non-zero hyperdifferential prime ideal, then it contains the Poincaré series $h=P_{q+1,1}$ of \cite{Ge}. This last result is the analogue of a crucial property proved by Nesterenko \cite{Nes} in characteristic zero in order to establish a multiplicity estimate. | |
| dc.identifier | https://arxiv.org/abs/math/0703842 | |
| dc.identifier | http://arxiv.org/abs/math/0703842 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126534 | |
| dc.subject | Number Theory | |
| dc.title | Hyperdifferential properties of Drinfeld quasi-modular forms | |
| dc.type | text |