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1. Introduction. Let k be an integer and N be a positive integer divisible by 4. If is a prime, denote by v a continuation of the usual-adic valuation on Q to a fixed algebraic closure. Let f be a modular form of weight k + 1/2 with respect to 0 (N) and Nebentypus character χ which has integral algebraic Fourier coefficients a(n), and put v (f) = inf n v(More)
We prove that the coefficients of certain weight −1/2 harmonic Maass forms are " traces " of singular moduli for weak Maass forms. To prove this theorem, we construct a theta lift from spaces of weight −2 harmonic weak Maass forms to spaces of weight −1/2 vector-valued harmonic weak Maass forms on Mp 2 (Z), a result which is of independent interest. We then(More)
For integers k ≥ 2, we study two differential operators on harmonic weak Maass forms of weight 2 − k. The operator ξ 2−k (resp. D k−1) defines a map to the space of weight k cusp forms (resp. weakly holomorphic modular forms). We leverage these operators to study coefficients of harmonic weak Maass forms. Although generic harmonic weak Maass forms are(More)