In this paper, the analogy of Bol's result to the several variable function case is discussed. One shows how to construct Siegel modular forms and Jacobi forms of higher degree, respectively, using Bol's result.
We investigate differential operators and their compatibility with subgroups of SL 2 (R) n . In particular, we construct Rankin-Cohen brackets for Hilbert modular forms, and more generally, multilinear differential operators on the space of Hilbert modular forms. As an application, we explicitly determine the RankinCohen bracket of a Hilbert-Eisenstein series and an arbitrary Hilbert modular form. We use this result to compute the Petersson inner product of such a bracket and a Hilbert modular cusp form.
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