Differential operators on Hilbert modular forms
نویسندگان
چکیده
We investigate differential operators and their compatibility with subgroups of SL2(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 Rankin– Cohen 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. © 2006 Elsevier Inc. All rights reserved. MSC: primary 11F55; secondary 11F41, 11F60
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