Algebraicity of higher Green functions at a CM point

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Item Type:	Article
Type of entry:	Secondary publication
Title:	Algebraicity of higher Green functions at a CM point
Language:	English
Date:	16 January 2025
Place of Publication:	Darmstadt
Year of primary publication:	October 2023
Place of primary publication:	Berlin ; Heidelberg
Publisher:	Springer
Journal or Publication Title:	Inventiones mathematicae
Volume of the journal:	234
Issue Number:	1
DOI:	10.26083/tuprints-00028366
Corresponding Links:	Publisher-DOI
Origin:	Secondary publication DeepGreen
Abstract:	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.
Status:	Publisher's Version
URN:	urn:nbn:de:tuda-tuprints-283660
Classification DDC:	500 Science and mathematics > 510 Mathematics
Divisions:	04 Department of Mathematics > Algebra
Date Deposited:	16 Jan 2025 13:50
Last Modified:	16 Jan 2025 13:50
SWORD Depositor:	Deep Green
URI:	https://tuprints.ulb.tu-darmstadt.de/id/eprint/28366
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