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arXiv 2204.013672022-04-04math.NT

四元数模形式所附L值的代数性

Algebraicity of L-values attached to Quaternionic Modular Forms

Thanasis Bouganis, Yubo Jin

备注：: 36
发表信息：: Can. J. Math.-J. Can. Math. 76 (2024) 638-679
DOI：: 10.4153/S0008414X23000184

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AI总结：

本文利用双倍方法证明四元数模形式L值的代数性，主要贡献是处理了对称空间为非管型的情形，并显式给出了双倍嵌入、陪集分解及基于CM点的代数性定义。

摘要：

本文证明了一些与四元数模形式相关的L值的代数性。我们遵循了相当成熟的双倍方法路径。我们的主要贡献在于纳入了相应对称空间为非管型的情形。我们使多个方面变得非常明确，例如双倍嵌入、陪集分解，以及通过CM点定义模形式代数性。

英文摘要：

In this paper we prove the algebraicity of some L-values attached to quaternionic modular forms. We follow the rather well established path of the doubling method. Our main contribution is that we include the case where the corresponding symmetric space is of non-tube type. We make various aspects very explicit such as, the doubling embedding, coset decomposition, and the definition of algebraicity of modular forms via CM points.

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