Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds

Detalhes bibliográficos
Autor(a) principal: Flaminio, Livio
Data de Publicação: 2015
Outros Autores: Cosentino, Salvatore
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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spelling 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 reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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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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