Drinfeld Quasi-Modular Forms of Higher Level
Abstract
We study the structure of the vector space of Drinfeld quasi-modular forms for congruence subgroups. We provide representations as polynomials in the false Eisenstein series with coefficients in the space of Drinfeld modular forms (the -expansion), and, whenever possible, as sums of hyperderivatives of Drinfeld modular forms. \\ Moreover, we introduce and study the double-slash operator, and use it to provide a well-posed definition for Hecke operators on Drinfeld quasi-modular forms. We characterize eigenforms and, for the special case of Hecke congruence subgroups , we give explicit formulas for the Hecke action on -expansions.
Keywords
Cite
@article{arxiv.2502.08263,
title = {Drinfeld Quasi-Modular Forms of Higher Level},
author = {Andrea Bandini and Maria Valentino and Sjoerd de Vries},
journal= {arXiv preprint arXiv:2502.08263},
year = {2025}
}
Comments
Additional results concerning associated polynomials, as well as Hecke operators and their eigenvalues, have been included. Furthermore, the notion of being holomorphic at infinity for a quasi-modular function is discussed in detail