%0 Journal Article
%T On three theorems of Folsom, Ono and Rhoades
%A Wadim Zudilin
%J Mathematics
%D 2013
%I arXiv
%R 10.1090/S0002-9939-2014-12364-1
%X In his deathbed letter to Hardy, Ramanujan gave a vague definition of a mock modular function: at each root of unity its asymptotics 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.
%U http://arxiv.org/abs/1309.2053v2