Vector-valued modular forms and the mock theta conjectures

Nickolas Andersen
2016 Research in Number Theory  
The mock theta conjectures are ten identities involving Ramanujan's fifth-order mock theta functions. The conjectures were proven by Hickerson in 1988 using q-series methods. Using methods from the theory of harmonic Maass forms, specifically work of Zwegers and Bringmann-Ono, Folsom reduced the proof of the mock theta conjectures to a finite computation. Both of these approaches involve proving the identities individually, relying on work of Andrews-Garvan. Here we give a unified proof of the
more » ... ified proof of the mock theta conjectures by realizing them as an equality between two nonholomorphic vector-valued modular forms which transform according to the Weil representation. We then show that the difference of these vectors lies in a zero-dimensional vector space. 0 1 6 ) 2 : 3 2
doi:10.1007/s40993-016-0062-6 fatcat:qde545c62befxfodzbauyclfdm