Universität zu Köln

Bruinier, Jan Hendrik, Ehlen, Stephan and Yang, Tonghai (2021). CM values of higher automorphic Green functions for orthogonal groups. Invent. Math., 225 (3). S. 693 - 786. HEIDELBERG: SPRINGER HEIDELBERG. ISSN 1432-1297

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Abstract

Gross and Zagier conjectured that the CM values (of certain Hecke translates) of the automorphic Green function G(s) (z(1), z(2)) 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 z(1) over all CM points of a fixed discriminant d(1) (twisted by a genus character), and allow in the second variable the evaluation at individual CM points of discriminant d(2). 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Bruinier, Jan Hendrik UNSPECIFIED UNSPECIFIED UNSPECIFIED Ehlen, Stephan UNSPECIFIED UNSPECIFIED UNSPECIFIED Yang, Tonghai UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-582029
DOI:	10.1007/s00222-021-01038-0
Journal or Publication Title:	Invent. Math.
Volume:	225
Number:	3
Page Range:	S. 693 - 786
Date:	2021
Publisher:	SPRINGER HEIDELBERG
Place of Publication:	HEIDELBERG
ISSN:	1432-1297
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/58202