Weakly holomorphic modular forms on $$\Gamma _{0}(4)$$ and Borcherds products on unitary group $$\mathrm{U}(2,1)$$

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 $$k\le -1$$ , and we make use of the basis elements for the case $$k=-1$$ to construct explicit Borcherds products on unitary group $$\mathrm{U}(2,1)$$ .