Abstract We explicitly construct modular forms on a 4-dimensional bounded symmetric domain of type IV based on the variation of the Hodge structures of K3 surfaces. We study the ring of our modular forms. Because of the Kneser conditions of the transcendental lattice of our family of K3 surfaces, our modular group has a good arithmetic property. Also, our results can be regarded as natural extensions of the result of [4] for Siegel modular forms from the viewpoint of K3 surfaces.

中文翻译：

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K3 曲面的反周期映射和具有 Kneser 条件的格子的模形式的构造

摘要 我们基于 K3 曲面的 Hodge 结构的变化，在类型 IV 的 4 维有界对称域上显式地构造了模形式。我们研究模块化形式的环。由于我们 K3 曲面族的超越点阵的 Kneser 条件，我们的模群具有良好的算术性质。此外，从 K3 曲面的角度来看，我们的结果可以看作是 [4] 对 Siegel 模形式的结果的自然扩展。