Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds
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Data de Publicação: | 2015 |
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Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/39085 |
Resumo: | 2010 Mathematics Subject Classification: Primary: 37C85, 37A17, 37A45; Secondary: 11K36, 11L07. |
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Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifoldsEquidistributionHeisenberg groupCohomological equationCiências Naturais::MatemáticasScience & Technology2010 Mathematics Subject Classification: Primary: 37C85, 37A17, 37A45; Secondary: 11K36, 11L07.We prove quantitative equidistribution results for actions of Abelian subgroups of the (2g + 1)-dimensional Heisenberg group acting on compact (2g + 1)-dimensional homogeneous nilmanifolds. The results are based on the study of the C∞-cohomology of the action of such groups, on tame estimates of the associated cohomological equations and on a renormalization method initially applied by Forni to surface flows and by Forni and the second author to other parabolic flows. As an application we obtain bounds for finite Theta sums defined by real quadratic forms in g variables, generalizing the classical results of Hardy and Littlewood [25, 26] and the optimal result of Fiedler, Jurkat, and Körner [17] to higher dimension.This work was partially done while L. Flaminio visited the Isaac Newton Institute in Cambridge, UK. He wishes to thank the Institute and the organizers of the program Interactions between Dynamics of Group Actions and Number Theory for their hospitality. L. Flaminio was supported in part by the Labex CEMPI (ANR-11-LABX-07). S. Cosentino was partially supported by CMAT - Centro de Matematica da Universidade do Minho, financed by the Strategic Project PEst-OE/MAT/UI0013/2014.American Institute of Mathematical Sciences (AIMS)Universidade do MinhoFlaminio, LivioCosentino, Salvatore2015-112015-11-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/39085eng1930-532X10.3934/jmd.2015.9.305http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=11898info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:31:23Zoai:repositorium.sdum.uminho.pt:1822/39085Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:26:39.616480Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds |
title |
Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds |
spellingShingle |
Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds Flaminio, Livio Equidistribution Heisenberg group Cohomological equation Ciências Naturais::Matemáticas Science & Technology |
title_short |
Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds |
title_full |
Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds |
title_fullStr |
Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds |
title_full_unstemmed |
Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds |
title_sort |
Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds |
author |
Flaminio, Livio |
author_facet |
Flaminio, Livio Cosentino, Salvatore |
author_role |
author |
author2 |
Cosentino, Salvatore |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Flaminio, Livio Cosentino, Salvatore |
dc.subject.por.fl_str_mv |
Equidistribution Heisenberg group Cohomological equation Ciências Naturais::Matemáticas Science & Technology |
topic |
Equidistribution Heisenberg group Cohomological equation Ciências Naturais::Matemáticas Science & Technology |
description |
2010 Mathematics Subject Classification: Primary: 37C85, 37A17, 37A45; Secondary: 11K36, 11L07. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015-11 2015-11-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1822/39085 |
url |
http://hdl.handle.net/1822/39085 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1930-532X 10.3934/jmd.2015.9.305 http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=11898 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
American Institute of Mathematical Sciences (AIMS) |
publisher.none.fl_str_mv |
American Institute of Mathematical Sciences (AIMS) |
dc.source.none.fl_str_mv |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799132754530533376 |