Hyperdifferential properties of Drinfeld quasi-modular forms

Details Hyperdifferential properties of Drinfeld quasi-modular forms Hyperdifferential properties of Drinfeld quasi-modular forms

2007-03-28

arxiv.org/abs/math/0703842v1

Mathematics

Number Theory

Scientific paper

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 Poincar\'e 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.

Affiliated with

Also associated with

No associations

Rating

Hyperdifferential properties of Drinfeld quasi-modular forms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hyperdifferential properties of Drinfeld quasi-modular forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hyperdifferential properties of Drinfeld quasi-modular forms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-272783