Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues

被引：0

作者：

Jan H. Bruinier

Ken Ono

Robert C. Rhoades

机构：

[1] Technische Universität Darmstadt,Fachbereich Mathematik

[2] University of Wisconsin,Department of Mathematics

来源：

Mathematische Annalen | 2008年 / 342卷

关键词：

Modular Form; Fourier Expansion; Eisenstein Series; Cusp Form; Principal Part;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

For integers k ≥ 2, we study two differential operators on harmonic weak Maass forms of weight 2 − k. The operator ξ2-k (resp. Dk-1) defines a map to the space of weight k cusp forms (resp. weakly holomorphic modular forms). We leverage these operators to study coefficients of harmonic weak Maass forms. Although generic harmonic weak Maass forms are expected to have transcendental coefficients, we show that those forms which are “dual” under ξ2-k to newforms with vanishing Hecke eigenvalues (such as CM forms) have algebraic coefficients. Using regularized inner products, we also characterize the image of Dk-1.

引用

页码：673 / 693

页数：20

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