چکیده (انگلیسی):

We construct an infinite family of half-integral weight Poincaré series coming from vector valued harmonic weak Maass forms, and investigate linear relations among the Poincaré series by applying a pairingbetween weakly holomorphic modular forms and harmonic weak Maass forms together with properties of Maass Poincaré series. We also show that the Poincaré series are characterized by the Fourier coef-ficients of half-integral weight cusp forms.