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The mock theta conjectures are ten identities involving Ramanujan'sfifth-order mock theta functions. The conjectures were proven by Hickerson in1988 using q-series methods. Using methods from the theory of harmonic Maassforms, specifically work of Zwegers and Bringmann-Ono, Folsom reduced the proofof the mock theta conjectures to a finite computation. Both of these approachesinvolve proving the identities individually, relying on work of Andrews-Garvan.Here we give a unified proof of the mock theta conjectures by realizing them asan equality between two nonholomorphic vector-valued modular forms whichtransform according to the Weil representation. We then show that thedifference of these vectors lies in a zero-dimensional vector space.

Vector-valued modular forms and the Mock Theta Conjectures