LARGE FOURIER COEFFICIENTS OF HALF-INTEGER WEIGHT MODULAR FORMS

This article is concerned with the Fourier coefficients of cusp forms (not necessarily eigenforms) of half-integer weight lying in the plus space. We give a soft proof that there are infinitely many fundamental discriminants D such that the Fourier coefficients evaluated at D are non-zero. By adapting the resonance method, we also demonstrate that such Fourier coefficients must take quite large values.