Differential operators on Hilbert modular forms |
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Authors: | YoungJu Choie Haesuk Kim |
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Institution: | a Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea b Department of Mathematics, University of North Texas, Denton, TX 76203, USA |
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Abstract: | We investigate differential operators and their compatibility with subgroups of SL2n(R). 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. |
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Keywords: | primary 11F55 secondary 11F41 11F60 |
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