[GS_M_NT] On the infinite product expansions of meromorphic modular forms
ABSTRACT
Many modular forms are usually expressed using Fourier expansions, but in some cases, such as the modular discriminant, it is more useful to express them using infinite product expansions. The most important result, initiated by Borcherds, associated with the infinite product expansion of modular forms, is that there exists a meromorphic modular form of integral weight for some character of SL(Z) with integer Fourier coefficients such that its exponents in the infinite product expansion are equal to the Fourier coefficients of a modular form of weight 1/2 on Γ0(4) satisfying Kohnen plus condition. In this talk, we introduce an operator acting on the exponents of the infinite product expansion of meromor-
phic modular forms and investigate its properties. This is joint work with Chang Heon Kim.