3 Arithmetical differential operators on nearly holomorphic Siegel modular forms

Abstract

3.1 Description of the Shimura differential operators 3.2 Nearly holomorphic Siegel modular forms 3.2.1 Algebraic nearly holomorphic Siegel modular forms 3.2.2 Formal expansions of nearly holomorphic forms. 3.2.3 Action of the U-operator. 3.3 Algebraic differential operators of Maass and Shimura 3.3.1 Differential operators on ℍ m . 3.3.2 The polynomial R m (z; r,β ). 3.3.3 Proof of Lemma 3.7 3.3.4 Action of the Shimura differential operator on formal Fourier expansions 3.3.5 Commutation of the Shimura operator with Hecke operators 3.4 Arithmetical variables of nearly holomorphic forms 3.4.1 Arithmetical nearly holomorphic Siegel modular forms 3.4.2 Action on Fourier expansion 3.4.3 Differentiation on monomials