HEAT OPERATORS ON MODULAR AND QUASIMODULAR POLYNOMIALS

Jacobi-like forms generalize Jacobi forms, and heat operators on Jacobi forms can be extended to heat operators on Jacobi-like forms. Quasimodular forms correspond to quasimodular polynomials and modular polynomials, and they can be lifted to Jacobi-like forms. We obtain an explicit formula for a differential operator on the space of quasimodular polynomials which is compatible with a heat operators on the space of Jacobi-like forms. We also determine a linear map on the space of modular polynomials that is compatible with this differential operator.

Automated summary

The article discusses the generalization of Jacobi forms to Jacobi-like forms, the correspondence between quasimodular forms and quasimodular and modular polynomials, as well as explicit formulas for a differential operator on quasimodular polynomials compatible with heat operators on Jacobi-like forms. It also describes a linear map on the space of modular polynomials compatible with this differential operator.