A note on eigenvalues of Hecke operators on Siegel modular forms of degree two

Kohnen, Winfried

doi:10.1090/S0002-9939-1991-1068125-2

A note on eigenvalues of Hecke operators on Siegel modular forms of degree two
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by Winfried Kohnen PDF

Proc. Amer. Math. Soc. 113 (1991), 639-642 Request permission

Abstract:

Let $F$ be a cuspidal Hecke eigenform of even weight $k$ on ${\operatorname {Sp} _4}(\mathbb {Z})$ with associated eigenvalues ${\lambda _m}(m \in \mathbb {N})$. Under the assumption that its first Fourier-Jacobi coefficient does not vanish it is proved that the abscissa of convergence of the Dirichlet series ${\sum _{m \geq 1}}\left | {{\lambda _m}} \right |{m^{ - s}}$ is less than or equal to $k$.

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Computations of Siegel modular forms of genus two