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.
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 show that spaces of vector-valued singular modular forms for principal congruence subgroups of the symplectic group Sp(n, Z) of integral weight k < n 2 < 2k are generated by suitable finite dimensional families of Siegel theta series. This is obtained as an application of some results concerning the action of trace operators on non-homogeneous theta series.
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