Zeros of modular forms of half integral weight

Abstract

We study canonical bases for spaces of weakly holomorphic modular forms of level 4 and weights in 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 Γ 0(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 Poincaré series, and show that for positive weights, a particular set of Fourier coefficients of cusp forms in this canonical basis cannot simultaneously vanish.