3.8 Article

HEAT OPERATORS ON MODULAR AND QUASIMODULAR POLYNOMIALS

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WYDAWNICTWO NAUKOWE UAM
DOI: 10.7169/facm/1978

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quasimodular forms; modular forms; heat operators; Jacobi-like forms

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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.
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.

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