Zeros of modular forms of half integral weight
We study canonical bases for spaces of weakly holomorphic modular forms of level 4 and weights in \mathbb {Z}\frac{1}{2}$Z+12 and show that almost all modular forms in these bases have the property that many of their zeros in a fundamental domain for \Gamma _0(4)$G0(4) lie on a lower boundary arc of the fundamental domain. Additionally, we show that at many places on this arc, the generating function for Hurwitz class numbers is equal to a particular mock modular Poincare series, and show that for positive weights, a particular set of Fourier coefficients of cusp forms in this canonical basis cannot simultaneously vanish.