Holomorphic projections and Ramanujan's mock theta functions

Abstract

We employ 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.

To appear in PNAS

References in corpus (2)

• Notes on the K3 Surface and the Mathieu group M_24
• Lectures on Quantum Black Holes

Cited by in corpus (15)

• Eichler-Selberg Type Identities for Mixed Mock Modular Forms
• Algebraic formulas for the coefficients of mock theta functions and Weyl vectors of Borcherds products
• A proof of the Thompson Moonshine Conjecture
• Proof of the Umbral Moonshine Conjecture
• Special values of shifted convolution Dirichlet series
• Vector-valued Hirzebruch-Zagier series and class number sums
• Polar harmonic Maaß forms and holomorphic projection
• Non-Holomorphic Ramanujan-type Congruences for Hurwitz Class Numbers
• Theta lifts for Lorentzian lattices and coefficients of mock theta functions
• Universal mock theta functions and two-variable Hecke-Rogers identities
• Picard rank jumps for K3 surfaces with bad reduction
• On recursions for coefficients of mock theta functions
• Local Maaß forms and Eichler--Selberg type relations for negative weight vector-valued mock modular forms
• A family of mock theta functions of weights 1/2 and 3/2 and their congruence properties
• Asymptotic bounds for special values of shifted convolution Dirichlet series