On Rankin-cohen Brackets for Siegel Modular Forms
نویسندگان
چکیده
We determine an explicit formula for a Rankin-Cohen bracket for Siegel modular forms of degree n on a certain subgroup of the symplectic group. Moreover, we lift that bracket via a Poincaré series to a Siegel cusp form on the full symplectic group.
منابع مشابه
Generalized Transvectants and Siegel Modular Forms
We introduce a differential operator invariant under the special linear group SL(2n, C), and, as a consequence, the symplectic group Sp(2n, C). Connections with generalized Rankin–Cohen brackets for Siegel modular forms of genus n are sketched.
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Classically, there are many interesting connections between differential operators and the theory of elliptic modular forms and many interesting results have been explored. In particular, it has been known for some time how to obtain an elliptic modular form from the derivatives ofN elliptic modular forms, which has already been studied in detail by R. Rankin in [9] and [10]. When N = 2, as a s...
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A~tract, In 1956, Rankin described which polynomials in the derivatives of modular forms are again modular forms, and in 1977, H Cohen defined for each n i> 0 a bilinear operation which assigns to two modular forms f and g of weight k and l a modular form If, g], of weight k + l + 2n. In the present paper we study these "Rankin-Cohen brackets" from t w o points of view. On the one hand we give ...
متن کاملSymplectic Transvectant and Siegel Modular Forms
We introduce a differential operator invariant under the symplectic group Sp(2n, C). A connection with a Rankin Cohen bracket for Siegel modular forms of genus n is sketched.
متن کاملRankin-Cohen Brackets and Invariant Theory
Using maps due to Ozeki and Broué-Enguehard between graded spaces of invariants for certain finite groups and the algebra of modular forms of even weight we equip these invariants spaces with a differential operator which gives them the structure of a Rankin-Cohen algebra. A direct interpretation of the Rankin-Cohen bracket in terms of transvectant for the group SL(2,C) is given.
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تاریخ انتشار 2005