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

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dc.creatorBruinier, Jan H.
dc.creatorOno, Ken
dc.creatorRhoades, Robert C.
dc.date2008-02-07
dc.date2009-01-26
dc.date.accessioned2026-07-07T12:33:59Z
dc.date.available2026-07-07T12:33:59Z
dc.descriptionFor integers $k\geq 2$, we study two differential operators on harmonic weak Maass forms of weight $2-k$. The operator $ξ_{2-k}$ (resp. $D^{k-1}$) 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 $ξ_{2-k}$ to newforms with vanishing Hecke eigenvalues (such as CM forms) have algebraic coefficients. Using regularized inner products, we also characterize the image of $D^{k-1}$.
dc.descriptionformerly "Differential operators and harmonic weak Maass forms"; Theorem 1.4 corrected
dc.identifierhttps://arxiv.org/abs/0802.0963
dc.identifierhttp://arxiv.org/abs/0802.0963
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217269
dc.subjectNumber Theory
dc.subject11F25, 11F30
dc.titleDifferential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues
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