On certain families of Drinfeld quasi-modular forms

TL;DR

This paper explores properties of Drinfeld quasi-modular forms, focusing on their vanishing orders and differential characteristics, advancing understanding of their structure in the function field setting.

Contribution

It provides partial results on the maximal vanishing order and differential properties of Drinfeld quasi-modular forms, addressing open problems in the field.

Findings

Partial bounds on the order of vanishing at infinity.

Characterization of differential properties for forms with maximal vanishing.

Progress towards solving open problems in Drinfeld quasi-modular forms.

Abstract

The aim of this paper is to describe some partial advances in the solution of the following two problems. Find the maximal order of vanishing at infinity of a non-zero Drinfeld quasi-modular form of given weight. Determine differential properties of a Drinfeld quasi-modular form of given weight and depth with maximal order of vanishing at infinity.