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We present completions of mock theta functions to harmonic weak Maass formsof weight $1/2$ and algebraic formulas for the coefficients of mock thetafunctions. We give several harmonic weak Maass forms of weight $1/2$ that havemock theta functions as their holomorphic part. Using these harmonic weak Maassforms and the Millson theta lift we compute finite algebraic formulas for thecoefficients of the appearing mock theta functions in terms of traces ofsingular moduli.

Completions and algebraic formulas for the coefficients of Ramanujan's mock theta functions