On three theorems of Folsom, Ono and Rhoades

In his deathbed letter to G.H. Hardy, Ramanujan gave a vague definition of a mock modular function: at each root of unity its asymptotic matches the one of a modular form, though a choice of the modular function depends on the root of unity. Recently Folsom, Ono and Rhoades have proved an elegant result about the match for a general family related to Dyson's rank (mock theta) function and the Andrews-Garvan crank (modular) function - the match with explicit formulae for implied O(1) constants. In this note we give another elementary proof of Ramanujan's original claim and outline some heuristics which may be useful for obtaining a new proof of the general Folsom-Ono-Rhoades theorem