This paper deals with two problems arising in the study of Drinfeld quasi-modular forms. The first problem is to find the maximal order of vanishing at infinity of a non-zero Drinfeld quasimodular form and leads to the notion of "extremal" quasi-modular form (highest possible order of vanishing for fixed weight and depth). The second problem is determining differential properties of extremal forms, leading to the notion of "differentially extremal" form. From our investigations, we will obtain an upper bound for the order of vanishing at infinity of non-zero Drinfeld quasimodular forms of small depths. The paper ends with a collection of tools used in the previous parts. The notion of "extremal" form is similar to one introduced by Kaneko and Koike in [M. Kaneko, M. Koike, On extremal quasimodular forms, Kyushu J. Math. 60 (2006) 457-470]. © 2009 Elsevier Inc. All rights reserved.

On certain families of Drinfeld quasi-modular forms / Bosser, V.; Pellarin, F.. - In: JOURNAL OF NUMBER THEORY. - ISSN 0022-314X. - 129:12(2009), pp. 2952-2990. [10.1016/j.jnt.2009.04.014]

On certain families of Drinfeld quasi-modular forms

Pellarin F.
2009

Abstract

This paper deals with two problems arising in the study of Drinfeld quasi-modular forms. The first problem is to find the maximal order of vanishing at infinity of a non-zero Drinfeld quasimodular form and leads to the notion of "extremal" quasi-modular form (highest possible order of vanishing for fixed weight and depth). The second problem is determining differential properties of extremal forms, leading to the notion of "differentially extremal" form. From our investigations, we will obtain an upper bound for the order of vanishing at infinity of non-zero Drinfeld quasimodular forms of small depths. The paper ends with a collection of tools used in the previous parts. The notion of "extremal" form is similar to one introduced by Kaneko and Koike in [M. Kaneko, M. Koike, On extremal quasimodular forms, Kyushu J. Math. 60 (2006) 457-470]. © 2009 Elsevier Inc. All rights reserved.
2009
Drinfeld modular forms; multiplicity estimates
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On certain families of Drinfeld quasi-modular forms / Bosser, V.; Pellarin, F.. - In: JOURNAL OF NUMBER THEORY. - ISSN 0022-314X. - 129:12(2009), pp. 2952-2990. [10.1016/j.jnt.2009.04.014]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1623689
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