TU Darmstadt / ULB / TUprints

CM values of higher automorphic Green functions for orthogonal groups

Bruinier, Jan Hendrik ; Ehlen, Stephan ; Yang, Tonghai (2024)
CM values of higher automorphic Green functions for orthogonal groups.
In: Inventiones mathematicae, 2021, 225 (3)
doi: 10.26083/tuprints-00023439
Article, Secondary publication, Publisher's Version

[img] Text
s00222-021-01038-0.pdf
Copyright Information: CC BY 4.0 International - Creative Commons, Attribution.

Download (954kB)
Item Type: Article
Type of entry: Secondary publication
Title: CM values of higher automorphic Green functions for orthogonal groups
Language: English
Date: 18 March 2024
Place of Publication: Darmstadt
Year of primary publication: September 2021
Place of primary publication: Berlin ; Heidelberg
Publisher: Springer
Journal or Publication Title: Inventiones mathematicae
Volume of the journal: 225
Issue Number: 3
DOI: 10.26083/tuprints-00023439
Corresponding Links:
Origin: Secondary publication DeepGreen
Abstract:

Gross and Zagier conjectured that the CM values (of certain Hecke translates) of the automorphic Green function Gs (z₁, z₂) for the elliptic modular group at positive integral spectral parameter s are given by logarithms of algebraic numbers in suitable class fields. We prove a partial average version of this conjecture, where we sum in the first variable z₁ over all CM points of a fixed discriminant d₁ (twisted by a genus character), and allow in the second variable the evaluation at individual CM points of discriminant d₂. This result is deduced from more general statements for automorphic Green functions on Shimura varieties associated with the group GSpin (n, 2). We also use our approach to prove a Gross–Kohnen–Zagier theorem for higher Heegner divisors on Kuga–Sato varieties over modular curves.

Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-234397
Additional Information:

Mathematics Subject Classification: 11G18, 11G15, 11F37

Classification DDC: 500 Science and mathematics > 510 Mathematics
Divisions: 04 Department of Mathematics > Algebra > Automorphic Forms, Number Theory, Algebraic Geometry
Date Deposited: 18 Mar 2024 13:40
Last Modified: 30 Apr 2024 09:33
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/23439
PPN: 517364999
Export:
Actions (login required)
View Item View Item