tau-recurrent sequences and modular forms

preprint2011arXivOpen access

Abstract

In this paper we deal with Drinfeld modular forms, defined and taking values in complete fields of positive characteristic. Our aim is to study a sequence of families of Drinfeld modular forms depending on a parameter t that produces, for certain values of t, several kinds of Eisenstein series considered by Gekeler. We obtain formulas involving these functions. To obtain our results, we introduce and discuss tau-linear recurrent sequences and deformations of vectorial modular forms in this setting.

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