Estimating the order of vanishing at infinity of Drinfeld quasi-modular forms

TL;DR

This paper develops a framework for deforming Drinfeld quasi-modular forms using Anderson's t-motives, leading to new algebraic structures and multiplicity estimates related to their behavior at infinity.

Contribution

It introduces a novel deformation approach for Drinfeld quasi-modular forms via Anderson's t-motives, revealing algebraic gradings and automorphisms.

Findings

Established a graded sub-algebra with a natural Z^2 x Z/(q-1)Z grading.

Derived multiplicity estimates from algebraic properties.

Connected deformations to the order of vanishing at infinity.

Abstract

We introduce and study certain deformations of Drinfeld quasi-modular forms by using rigid analytic trivialisations of corresponding Anderson's t-motives. We show that a sub-algebra of these deformations has a natural graduation by the group Z^2 x Z/(q-1)Z and an homogeneous automorphism, and we deduce from this and other properties multiplicity estimates.