Algebraicity of higher Green functions at a CM point

• 成果类型: Article
• 署名作者: Li, Yingkun
• 署名单位: Technical University of Darmstadt
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-023-01205-5
• 发表日期: 2023
• 页码: 375-418
• 关键词: faltings heights; heegner points; maass forms; derivatives; VALUES; cycles; VARIETIES

摘要

In this paper, we investigate the algebraic nature of the value of a higher Green function on an orthogonal Shimura variety at a single CM point. This is motivated by a conjecture of Gross and Zagier in the setting of higher Green functions on the product of two modular curves. In the process, we will study analogue of harmonic Maass forms in the setting of Hilbert modular forms, and obtain results concerning the arithmetic of their holomorphic part Fourier coefficients. As a consequence, we answer a question of Zagier in his 1986 ICM proceeding.