Weakly holomorphic modular forms on Gamma_{0}(4) and Borcherds products on unitary group U(2,1)

Abstract: In this note, we construct canonical bases for the spaces of weakly holomorphic modular forms with poles supported at the cusp \(\infty\) for \(\Gamma_{0}(4)\) of integral weight \(k\) for \(k \leq −1\), and we make use of the basis elements for the case \(k = −1\) to construct explicit Borcherds products on unitary group \(U(2, 1)\).