Let F and G be Siegel cusp forms for \({\mathrm{Sp}}_4({{\mathbb {Z}}})\) and weights \(k_1, k_2\), respectively. Also let F and G be Hecke eigenforms lying in distinct eigen spaces. Further suppose that neither F nor G is a Saito–Kurokawa lift. In this article, we study simultaneous arithmetic behaviour of Hecke eigenvalues of these Hecke eigenforms.

中文翻译：

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Siegel尖点形式二阶Hecke特征值的算术行为

令F和G分别为\（{\ mathrm {Sp}} _ 4（{{\ mathbb {Z}}}）\）和权重\（k_1，k_2 \）的Siegel尖点形式。还让F和G为位于不同特征空间中的Hecke特征形。进一步假设F和G都不是斋藤-黑川电梯。在本文中，我们研究了这些Hecke特征形的Hecke特征值的同时算术行为。