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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/55427
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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 Técnicas2025-09-03T09:50:34Zoai: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:34982025-09-03 09:50:34.622CONICET 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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13.13397 |