Bruinier, Jan Hendrik ; Ehlen, Stephan ; Yang, Tonghai (2021)
CM values of higher automorphic Green functions for orthogonal groups.
In: Inventiones mathematicae, 225 (3)
doi: 10.1007/s00222-021-01038-0
Artikel, Bibliographie
Dies ist die neueste Version dieses Eintrags.
Kurzbeschreibung (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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2021 |
| Autor(en): | Bruinier, Jan Hendrik ; Ehlen, Stephan ; Yang, Tonghai |
| Art des Eintrags: | Bibliographie |
| Titel: | CM values of higher automorphic Green functions for orthogonal groups |
| Sprache: | Englisch |
| Publikationsjahr: | September 2021 |
| Ort: | Berlin ; Heidelberg |
| Verlag: | Springer |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Inventiones mathematicae |
| Jahrgang/Volume einer Zeitschrift: | 225 |
| (Heft-)Nummer: | 3 |
| DOI: | 10.1007/s00222-021-01038-0 |
| Zugehörige Links: | |
| Kurzbeschreibung (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. |
| Zusätzliche Informationen: | Mathematics Subject Classification: 11G18, 11G15, 11F37 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Algebra 04 Fachbereich Mathematik > Algebra > Automorphe Formen, Zahlentheorie, Algebraische Geometrie |
| Hinterlegungsdatum: | 19 Mär 2024 10:50 |
| Letzte Änderung: | 19 Mär 2024 10:50 |
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Verfügbare Versionen dieses Eintrags
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CM values of higher automorphic Green functions for orthogonal groups. (deposited 18 Mär 2024 13:40)
- CM values of higher automorphic Green functions for orthogonal groups. (deposited 19 Mär 2024 10:50) [Gegenwärtig angezeigt]
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