title: Holomorphic projections and Ramanujan's mock theta functions.
abstract: We use spectral methods of automorphic forms to establish a holomorphic projection operator for tensor products of vector-valued harmonic weak Maass forms and vector-valued modular forms. We apply this operator to discover simple recursions for Fourier series coefficients of Ramanujan's mock theta functions.
authors.affiliation: Mathematics Department, Eidgenössische Technische Hochschule Zürich, 8092 Zurich, Switzerland.
authors.forename: Özlem
authors.initials: Ö
authors.lastname: Imamoğlu
authors.forename: Martin
authors.initials: M
authors.lastname: Raum
authors.forename: Olav K
authors.initials: OK
authors.lastname: Richter
mesh_terms: D005583:Fourier Analysis; D008433:Mathematics; D008962:Models, Theoretical