On the injectivity of the Kudla-Millson lift and surjectivity of the Borcherds lift

We consider the Kudla-Millson lift from elliptic modular forms of weight (p+q)/2 to closed q-forms on locally symmetric spaces corresponding to the orthogonal group O(p,q). We study the L²-norm of the lift following the Rallis inner product formula. We compute the contribution at the Archimedian pla...

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Detalles Bibliográficos
Autores: Bruinier, Jan H., Funke, J.
Tipo de recurso: artículo
Fecha de publicación:2006
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:44224
Acceso en línea:https://ddd.uab.cat/record/44224
Access Level:acceso abierto
Palabra clave:Grups discontinus
Formes automòrfiques
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spelling On the injectivity of the Kudla-Millson lift and surjectivity of the Borcherds liftBruinier, Jan H.Funke, J.Grups discontinusFormes automòrfiquesWe consider the Kudla-Millson lift from elliptic modular forms of weight (p+q)/2 to closed q-forms on locally symmetric spaces corresponding to the orthogonal group O(p,q). We study the L²-norm of the lift following the Rallis inner product formula. We compute the contribution at the Archimedian place. For locally symmetric spaces associated to even unimodular lattices, we obtain an explicit formula for the L²-norm of the lift, which often implies that the lift is injective. For O(p,2) we discuss how such injectivity results imply the surjectivity of the Borcherds lift.Centre de Recerca MatemàticaCentre de Recerca Matemàtica 22006-01-0120062006-01-01Articlehttp://purl.org/coar/resource_type/c_6501AOhttp://purl.org/coar/version/c_b1a7d7d4d402bcceinfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/44224reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.https://creativecommons.org/licenses/by-nc-nd/2.5/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:442242026-06-06T12:50:31Z
dc.title.none.fl_str_mv On the injectivity of the Kudla-Millson lift and surjectivity of the Borcherds lift
title On the injectivity of the Kudla-Millson lift and surjectivity of the Borcherds lift
spellingShingle On the injectivity of the Kudla-Millson lift and surjectivity of the Borcherds lift
Bruinier, Jan H.
Grups discontinus
Formes automòrfiques
title_short On the injectivity of the Kudla-Millson lift and surjectivity of the Borcherds lift
title_full On the injectivity of the Kudla-Millson lift and surjectivity of the Borcherds lift
title_fullStr On the injectivity of the Kudla-Millson lift and surjectivity of the Borcherds lift
title_full_unstemmed On the injectivity of the Kudla-Millson lift and surjectivity of the Borcherds lift
title_sort On the injectivity of the Kudla-Millson lift and surjectivity of the Borcherds lift
dc.creator.none.fl_str_mv Bruinier, Jan H.
Funke, J.
author Bruinier, Jan H.
author_facet Bruinier, Jan H.
Funke, J.
author_role author
author2 Funke, J.
author2_role author
dc.contributor.none.fl_str_mv Centre de Recerca Matemàtica
dc.subject.none.fl_str_mv Grups discontinus
Formes automòrfiques
topic Grups discontinus
Formes automòrfiques
description We consider the Kudla-Millson lift from elliptic modular forms of weight (p+q)/2 to closed q-forms on locally symmetric spaces corresponding to the orthogonal group O(p,q). We study the L²-norm of the lift following the Rallis inner product formula. We compute the contribution at the Archimedian place. For locally symmetric spaces associated to even unimodular lattices, we obtain an explicit formula for the L²-norm of the lift, which often implies that the lift is injective. For O(p,2) we discuss how such injectivity results imply the surjectivity of the Borcherds lift.
publishDate 2006
dc.date.none.fl_str_mv 2
2006-01-01
2006
2006-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AO
http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/44224
url https://ddd.uab.cat/record/44224
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/2.5/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
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eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Centre de Recerca Matemàtica
publisher.none.fl_str_mv Centre de Recerca Matemàtica
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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