Estimates for dimensions of spaces of Siegel modular cusp forms
The authors give upper bounds for the dimension of the space \(S^k_n\) of Siegel cusp forms of degree \(n\) and weight \(k\). In particular, they provide various sets of Fourier-Jacobi coefficients, whose vanishing implies that the associated \(f\in S^k_n\) is identically zero. This approach generalizes Siegel's and Eichler's methods. As an example they are able to show that the Siegel theta series of degree \(n\) attached to the lattices \(E_8\oplus E_8\) and \(D^+_{16}\) coincide if and only if \(n\leq 3\) by computing just one Fourier coefficient.
scientific article; zbMATH DE number 977875
scientific article