A Note on the Non-vanishing of Poincaré Series

This is a brief survey of methods for studying the non-vanishing of cusp forms defined by Poincaré series. In particular, we give an overview of various known results on the non-vanishing of the following three families of cuspidal Poincaré series of integral weight on the upper half-plane \( {\mathcal {H}} \) : the classical holomorphic Poincaré series of exponential type, the Poincaré series of elliptic type, and the Poincaré series used by Kohnen for studying the non-vanishing on average of Hecke \( L \) -functions of cusp forms for \( {\mathrm {SL}}_2({\mathbb {Z}}) \) .