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

摘要

In this note, we construct canonical bases for the spaces of weakly holomorphic modular forms with poles supported at the cusp $$infty $$ ∞ for $$Gamma _{0}(4)$$ Γ 0 ( 4 ) of integral weight k for $$kle -1$$ k ≤ - 1 , and we make use of the basis elements for the case $$k=-1$$ k = - 1 to construct explicit Borcherds products on unitary group $$mathrm{U}(2,1)$$ U ( 2 , 1 ) .