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

Author: Winfried Kohnen
Journal: Proc. Amer. Math. Soc. 113 (1991), 639-642
MSC: Primary 11F60; Secondary 11F46, 11F66
MathSciNet review: 1068125
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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\vert {{\lambda _m}} \right\vert{m^{ - s}}$ is less than or equal to $ k$.

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Article copyright: © Copyright 1991 American Mathematical Society