Duality involving the mock theta function f ( q )

We show that the coefficients of Ramanujan's mock theta function f ( q ) are the first non‐trivial coefficients of a canonical sequence of modular forms. This fact follows from a duality which equates coefficients of the holomorphic projections of certain weight 1/2 Maass forms with coefficients of certain weight 3/2 modular forms. This work depends on the theory of Poincaré series, and a modification of an argument of Goldfeld and Sarnak on Kloosterman–Selberg zeta functions.