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 ∞ for 0 (4) of integral weight k for k ≤ −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).