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

Federico Pellarin (1)

1 ICJ - Institut Camille Jordan

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.

Mots clés: Drinfeld quasi-modular forms; multiplicity estimates; function fields of positive characteristic

Domaines: Théorie des nombres [math.NT]

Federico Pellarin. Estimating the order of vanishing at infinity of Drinfeld quasi-modular forms. Journal für die reine und angewandte Mathematik, 2012, 2014 (687), pp.1-42. ⟨10.1515/crelle-2012-0048⟩. ⟨hal-00407549v3⟩