On absolutely normal and continued fraction normal numbers

Autores
Becher, Veronica Andrea; Yuhjtman, Sergio Andrés
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We give a construction of a real number that is normal to all integer bases and continued fraction normal. The computation of the firstn digits of its continued fraction expansion performs in the order ofn^4 mathematical operations. The construction works by defining successive refinements of appropriate subintervals to achieve, in the limit, simple normality to all integer bases and continued fraction normality. The main difficulty is to control the length of these subintervals. To achieve this we adapt and combine known metric theorems on continued fractions and on expansions in integers bases.
Fil: Becher, Veronica Andrea. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Yuhjtman, Sergio Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
NORMAL NUMBERS
POLYNOMIAL TIME ALGORITHM
CONTINUED FRACTIONS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/55427
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On absolutely normal and continued fraction normal numbersBecher, Veronica AndreaYuhjtman, Sergio AndrésNORMAL NUMBERSPOLYNOMIAL TIME ALGORITHMCONTINUED FRACTIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We give a construction of a real number that is normal to all integer bases and continued fraction normal. The computation of the firstn digits of its continued fraction expansion performs in the order ofn^4 mathematical operations. The construction works by defining successive refinements of appropriate subintervals to achieve, in the limit, simple normality to all integer bases and continued fraction normality. The main difficulty is to control the length of these subintervals. To achieve this we adapt and combine known metric theorems on continued fractions and on expansions in integers bases.Fil: Becher, Veronica Andrea. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Yuhjtman, Sergio Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaOxford University Press2017-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/55427Becher, Veronica Andrea; Yuhjtman, Sergio Andrés; On absolutely normal and continued fraction normal numbers; Oxford University Press; International Mathematics Research Notices; 12-2017; 1-261073-7928CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1704.03622info:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnx297info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/advance-article-abstract/doi/10.1093/imrn/rnx297/4810650?redirectedFrom=fulltextinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:45:38Zoai:ri.conicet.gov.ar:11336/55427instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:45:39.204CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On absolutely normal and continued fraction normal numbers
title On absolutely normal and continued fraction normal numbers
spellingShingle On absolutely normal and continued fraction normal numbers
Becher, Veronica Andrea
NORMAL NUMBERS
POLYNOMIAL TIME ALGORITHM
CONTINUED FRACTIONS
title_short On absolutely normal and continued fraction normal numbers
title_full On absolutely normal and continued fraction normal numbers
title_fullStr On absolutely normal and continued fraction normal numbers
title_full_unstemmed On absolutely normal and continued fraction normal numbers
title_sort On absolutely normal and continued fraction normal numbers
dc.creator.none.fl_str_mv Becher, Veronica Andrea
Yuhjtman, Sergio Andrés
author Becher, Veronica Andrea
author_facet Becher, Veronica Andrea
Yuhjtman, Sergio Andrés
author_role author
author2 Yuhjtman, Sergio Andrés
author2_role author
dc.subject.none.fl_str_mv NORMAL NUMBERS
POLYNOMIAL TIME ALGORITHM
CONTINUED FRACTIONS
topic NORMAL NUMBERS
POLYNOMIAL TIME ALGORITHM
CONTINUED FRACTIONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We give a construction of a real number that is normal to all integer bases and continued fraction normal. The computation of the firstn digits of its continued fraction expansion performs in the order ofn^4 mathematical operations. The construction works by defining successive refinements of appropriate subintervals to achieve, in the limit, simple normality to all integer bases and continued fraction normality. The main difficulty is to control the length of these subintervals. To achieve this we adapt and combine known metric theorems on continued fractions and on expansions in integers bases.
Fil: Becher, Veronica Andrea. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Yuhjtman, Sergio Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description We give a construction of a real number that is normal to all integer bases and continued fraction normal. The computation of the firstn digits of its continued fraction expansion performs in the order ofn^4 mathematical operations. The construction works by defining successive refinements of appropriate subintervals to achieve, in the limit, simple normality to all integer bases and continued fraction normality. The main difficulty is to control the length of these subintervals. To achieve this we adapt and combine known metric theorems on continued fractions and on expansions in integers bases.
publishDate 2017
dc.date.none.fl_str_mv 2017-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/55427
Becher, Veronica Andrea; Yuhjtman, Sergio Andrés; On absolutely normal and continued fraction normal numbers; Oxford University Press; International Mathematics Research Notices; 12-2017; 1-26
1073-7928
CONICET Digital
CONICET
url http://hdl.handle.net/11336/55427
identifier_str_mv Becher, Veronica Andrea; Yuhjtman, Sergio Andrés; On absolutely normal and continued fraction normal numbers; Oxford University Press; International Mathematics Research Notices; 12-2017; 1-26
1073-7928
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1704.03622
info:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnx297
info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/advance-article-abstract/doi/10.1093/imrn/rnx297/4810650?redirectedFrom=fulltext
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Oxford University Press
publisher.none.fl_str_mv Oxford University Press
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.069144

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