3:00 pm

Tuesday, 3rd Sep 2013

V205, Mathematics Building

Prof Wadim Zudilin

(CARMA, The University of Newcastle)

Mock theta functions

In his deathbed letter to G.H. 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. In my talk I will outline some heuristics and elementary ingredients of the proof.