论文标题
模块化线性差分运算符和广义的Rankin-Cohen支架
Modular Linear Differential Operators and Generalized Rankin-Cohen Brackets
论文作者
论文摘要
本文的目的是为任何顺序的模块化线性差分运算符提供表达式。特别是，我们表明它们都可以用兰金·科恩支架和Kaneko和Koike发现的Rankin-Cohen支架和改良的Rankin-Cohen支架来描述。我们还根据规范定义的较高的Serre衍生物以及Rankin-Cohen括号的扩展以及对半模形形式和几乎全体形态模块化形式的扩展，对MLDOS进行了更多统一的描述。这些描述中的最后一个涉及全体形态投影图。该论文还包括一些关于$ sl_2（\ mathbb {r}）$的cooCompact和非相结合亚组的一般结果
The aim in this paper is to give expressions for modular linear differential operators of any order. In particular, we show that they can all be described in terms of Rankin-Cohen brackets and a modified Rankin-Cohen bracket found by Kaneko and Koike. We also give more uniform descriptions of MLDOs in terms of canonically defined higher Serre derivatives and an extension of Rankin-Cohen brackets, as well as in terms of quasimodular forms and almost holomorphic modular forms. The last of these descriptions involves the holomorphic projection map. The paper also includes some general results on the theory of quasimodular forms on both cocompact and non-cocompact subgroups of $SL_2(\mathbb{R})$, as well as a slight sharpening of a theorem of Martin and Royer on Rankin-Cohen brackets of quasimodular forms
