Jan H. Bruinier

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In this paper we study the distribution of the coefficients a(n) of half integral weight modular forms modulo odd integers M . As a consequence we obtain improvements of indivisibility results for the central critical values of quadratic twists of L-functions associated with integral weight newforms established in [O-S]. Moreover, we find a simple criterion(More)
For integers k ≥ 2, we study two differential operators on harmonic weak Maass forms of weight 2 − k. The operator ξ2−k (resp. D) 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 expected(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 vectorvalued harmonic weak Maass forms on Mp2(Z), a result which is of independent interest. We then(More)
Let j(z) = q−1 + 744 + 196884q + · · · denote the usual elliptic modular function on SL2(Z) (q := e throughout). We shall refer to a complex number τ of the form τ = −b+ √ b2−4ac 2a with a, b, c ∈ Z, gcd(a, b, c) = 1 and b −4ac < 0 as a Heegner point, and we denote its discriminant by the integer dτ := b − 4ac. The values of j at such points are known as(More)