On certain families of Drinfeld quasi-modular forms
On certain families of Drinfeld quasi-modular forms
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关于 Drinfeld 拟模形式的某些族
DOI：
10.1016/j.jnt.2009.04.014
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发表时间：
2009
影响因子：
0.7
通讯作者：
F. Pellarin
中科院分区：
文献类型：
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作者：
V. Bosser;F. Pellarin
本文讨论了 Drinfeld 拟模形式研究中出现的两个问题。第一个问题是找到非零 Drinfeld 拟模形式的无穷远消失的最大阶数，并引出“极值”拟模形式的概念（固定重量和深度的消失的最高可能阶数）。第二个问题是确定极值形式的微分性质，从而产生了“微分极值”形式的概念。通过我们的研究，我们将获得小深度的非零 Drinfeld 拟模形式无穷大消失阶数的上限。本文最后提供了前面部分中使用的工具集合。 “极值”形式的概念与 Kaneko 和 Koike 在 [M. Kaneko, M. Koike，关于极值拟模形式，Kyushu J. Math。 60（2006）457-470]。
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 quasi-modular 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 quasi-modular 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].
DOI：
--
发表时间：
2010
期刊：
影响因子：
--
作者：
Shunsuke Takagi;Ken-ichi Yoshida;Masanobu Kaneko
通讯作者：
Masanobu Kaneko