Lattice points in elliptic paraboloids

We consider the lattice point problem corresponding to a family of elliptic paraboloids in Rd with d ≥ 3 and we prove the expected to be optimal exponent, improving previous results. This is especially noticeable for d = 3 because the optimal exponent is conjectural even for the sphere. We also trea...

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Detalles Bibliográficos
Autores: Chamizo Lorente, Fernando|||0000-0003-2793-7920, Pastor, Carlos
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:200755
Acceso en línea:https://ddd.uab.cat/record/200755
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6311912
Access Level:acceso abierto
Palabra clave:Elliptic paraboloids
Lattice point problem
Exponential sums
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spelling Lattice points in elliptic paraboloidsChamizo Lorente, Fernando|||0000-0003-2793-7920Pastor, CarlosElliptic paraboloidsLattice point problemExponential sumsWe consider the lattice point problem corresponding to a family of elliptic paraboloids in Rd with d ≥ 3 and we prove the expected to be optimal exponent, improving previous results. This is especially noticeable for d = 3 because the optimal exponent is conjectural even for the sphere. We also treat some aspects of the case d = 2, getting for a simple parabolic region an Ω-result that is unknown for the classical circle and divisor problems. 22019-01-0120192019-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/200755https://dx.doi.org/urn:doi:10.5565/PUBLMAT6311912reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2014-56350-Popen accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2007552026-06-06T12:50:31Z
dc.title.none.fl_str_mv Lattice points in elliptic paraboloids
title Lattice points in elliptic paraboloids
spellingShingle Lattice points in elliptic paraboloids
Chamizo Lorente, Fernando|||0000-0003-2793-7920
Elliptic paraboloids
Lattice point problem
Exponential sums
title_short Lattice points in elliptic paraboloids
title_full Lattice points in elliptic paraboloids
title_fullStr Lattice points in elliptic paraboloids
title_full_unstemmed Lattice points in elliptic paraboloids
title_sort Lattice points in elliptic paraboloids
dc.creator.none.fl_str_mv Chamizo Lorente, Fernando|||0000-0003-2793-7920
Pastor, Carlos
author Chamizo Lorente, Fernando|||0000-0003-2793-7920
author_facet Chamizo Lorente, Fernando|||0000-0003-2793-7920
Pastor, Carlos
author_role author
author2 Pastor, Carlos
author2_role author
dc.subject.none.fl_str_mv Elliptic paraboloids
Lattice point problem
Exponential sums
topic Elliptic paraboloids
Lattice point problem
Exponential sums
description We consider the lattice point problem corresponding to a family of elliptic paraboloids in Rd with d ≥ 3 and we prove the expected to be optimal exponent, improving previous results. This is especially noticeable for d = 3 because the optimal exponent is conjectural even for the sphere. We also treat some aspects of the case d = 2, getting for a simple parabolic region an Ω-result that is unknown for the classical circle and divisor problems.
publishDate 2019
dc.date.none.fl_str_mv 2
2019-01-01
2019
2019-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
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dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/200755
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6311912
url https://ddd.uab.cat/record/200755
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6311912
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2014-56350-P
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
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eu_rights_str_mv openAccess
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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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