On the construction of absolutely normal numbers
- Autores
- Aistleitner, Christoph; Becher, Veronica Andrea; Scheerer, Adrian-Maria; Slaman, Theodore A.
- Año de publicación
- 2017
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We give a construction of an absolutely normal real number x such that for every integer b greater than or equal to 2, the discrepancy of the first N terms of the sequence (bnx mod 1)n≥0 is of asymptotic order O(N−1/2). This is below the order of discrepancy which holds for almost all real numbers. Even the existence of absolutely normal numbers having a discrepancy of such a small asymptotic order was not known before.
Fil: Aistleitner, Christoph. Technical University Graz; Austria
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: Scheerer, Adrian-Maria. Technical University Graz; Austria
Fil: Slaman, Theodore A.. University of California at Berkeley; Estados Unidos - Materia
-
DISCREPANCY
NORMAL NUMBERS
UNIFORM DISTRIBUTION - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/60326
Ver los metadatos del registro completo
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On the construction of absolutely normal numbersAistleitner, ChristophBecher, Veronica AndreaScheerer, Adrian-MariaSlaman, Theodore A.DISCREPANCYNORMAL NUMBERSUNIFORM DISTRIBUTIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We give a construction of an absolutely normal real number x such that for every integer b greater than or equal to 2, the discrepancy of the first N terms of the sequence (bnx mod 1)n≥0 is of asymptotic order O(N−1/2). This is below the order of discrepancy which holds for almost all real numbers. Even the existence of absolutely normal numbers having a discrepancy of such a small asymptotic order was not known before.Fil: Aistleitner, Christoph. Technical University Graz; AustriaFil: 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: Scheerer, Adrian-Maria. Technical University Graz; AustriaFil: Slaman, Theodore A.. University of California at Berkeley; Estados UnidosPolish Academy of Sciences. Institute of Mathematics2017-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/60326Aistleitner, Christoph; Becher, Veronica Andrea; Scheerer, Adrian-Maria; Slaman, Theodore A.; On the construction of absolutely normal numbers; Polish Academy of Sciences. Institute of Mathematics; Acta Arithmetica; 180; 4; 12-2017; 333-3460065-1036CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.4064/aa170213-5-8info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:07:19Zoai:ri.conicet.gov.ar:11336/60326instacron: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 10:07:19.594CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
On the construction of absolutely normal numbers |
| title |
On the construction of absolutely normal numbers |
| spellingShingle |
On the construction of absolutely normal numbers Aistleitner, Christoph DISCREPANCY NORMAL NUMBERS UNIFORM DISTRIBUTION |
| title_short |
On the construction of absolutely normal numbers |
| title_full |
On the construction of absolutely normal numbers |
| title_fullStr |
On the construction of absolutely normal numbers |
| title_full_unstemmed |
On the construction of absolutely normal numbers |
| title_sort |
On the construction of absolutely normal numbers |
| dc.creator.none.fl_str_mv |
Aistleitner, Christoph Becher, Veronica Andrea Scheerer, Adrian-Maria Slaman, Theodore A. |
| author |
Aistleitner, Christoph |
| author_facet |
Aistleitner, Christoph Becher, Veronica Andrea Scheerer, Adrian-Maria Slaman, Theodore A. |
| author_role |
author |
| author2 |
Becher, Veronica Andrea Scheerer, Adrian-Maria Slaman, Theodore A. |
| author2_role |
author author author |
| dc.subject.none.fl_str_mv |
DISCREPANCY NORMAL NUMBERS UNIFORM DISTRIBUTION |
| topic |
DISCREPANCY NORMAL NUMBERS UNIFORM DISTRIBUTION |
| 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 an absolutely normal real number x such that for every integer b greater than or equal to 2, the discrepancy of the first N terms of the sequence (bnx mod 1)n≥0 is of asymptotic order O(N−1/2). This is below the order of discrepancy which holds for almost all real numbers. Even the existence of absolutely normal numbers having a discrepancy of such a small asymptotic order was not known before. Fil: Aistleitner, Christoph. Technical University Graz; Austria 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: Scheerer, Adrian-Maria. Technical University Graz; Austria Fil: Slaman, Theodore A.. University of California at Berkeley; Estados Unidos |
| description |
We give a construction of an absolutely normal real number x such that for every integer b greater than or equal to 2, the discrepancy of the first N terms of the sequence (bnx mod 1)n≥0 is of asymptotic order O(N−1/2). This is below the order of discrepancy which holds for almost all real numbers. Even the existence of absolutely normal numbers having a discrepancy of such a small asymptotic order was not known before. |
| 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/11336/60326 Aistleitner, Christoph; Becher, Veronica Andrea; Scheerer, Adrian-Maria; Slaman, Theodore A.; On the construction of absolutely normal numbers; Polish Academy of Sciences. Institute of Mathematics; Acta Arithmetica; 180; 4; 12-2017; 333-346 0065-1036 CONICET Digital CONICET |
| url |
http://hdl.handle.net/11336/60326 |
| identifier_str_mv |
Aistleitner, Christoph; Becher, Veronica Andrea; Scheerer, Adrian-Maria; Slaman, Theodore A.; On the construction of absolutely normal numbers; Polish Academy of Sciences. Institute of Mathematics; Acta Arithmetica; 180; 4; 12-2017; 333-346 0065-1036 CONICET Digital CONICET |
| dc.language.none.fl_str_mv |
eng |
| language |
eng |
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info:eu-repo/semantics/altIdentifier/doi/10.4064/aa170213-5-8 |
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info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
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openAccess |
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https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
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application/pdf application/pdf |
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Polish Academy of Sciences. Institute of Mathematics |
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Polish Academy of Sciences. Institute of Mathematics |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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13.13397 |