On the ring structure of automorphic forms and differential operators

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Our aim on this project is to determine the structure of automorphic forms by using differential operators. In this two years, we have the following two results :(1) On the structure of Hilbert modular forms with respect to a real quadratic field with small discriminant, we have a structure theorem when the difference of the weight is small.(2) On the structure of vector valued Siegel modular forms of degree 2, we have a structure theorem when the discrete subgroup is in a congruent subgroup with a small level.