A weak multiplicity-one theorem for Siegel modular forms.
Let \(F\), \(G\) be two Siegel modular forms of degree \(n\) with respect to some congruence subgroup \(F_{n,0}(l)\) and some character. Suppose that \(F\), \(G\) are eigenforms with respect to the Hecke operator \(T_n(p)\), \(p\) prime, with the same eigenvalues. If their Fourier coefficients agree on all primitive lattices and 0, then \(F=G\). The result generalizes the case \(n=2\) by \textit{S. Breulmann} and \textit{W. Kohnen} [Nagoya Math. J. 155, 153--166 (1999; Zbl 0936.11030)]. The proof is quite different and involves only elementary algebraic arguments.
scientific article; zbMATH DE number 2101115