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dc.contributor.author
Aistleitner, Christoph  
dc.contributor.author
Becher, Veronica Andrea  
dc.contributor.author
Scheerer, Adrian-Maria  
dc.contributor.author
Slaman, Theodore A.  
dc.date.available
2018-09-19T19:43:11Z  
dc.date.issued
2017-12  
dc.identifier.citation
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  
dc.identifier.issn
0065-1036  
dc.identifier.uri
http://hdl.handle.net/11336/60326  
dc.description.abstract
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.  
dc.format
application/pdf  
dc.language.iso
eng  
dc.publisher
Polish Academy of Sciences. Institute of Mathematics  
dc.rights
info:eu-repo/semantics/openAccess  
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/  
dc.subject
Discrepancy  
dc.subject
Normal Numbers  
dc.subject
Uniform Distribution  
dc.subject.classification
Matemática Pura  
dc.subject.classification
Matemáticas  
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS  
dc.title
On the construction of absolutely normal numbers  
dc.type
info:eu-repo/semantics/article  
dc.type
info:ar-repo/semantics/artículo  
dc.type
info:eu-repo/semantics/publishedVersion  
dc.date.updated
2018-09-17T19:37:49Z  
dc.journal.volume
180  
dc.journal.number
4  
dc.journal.pagination
333-346  
dc.journal.pais
Polonia  
dc.journal.ciudad
Varsovia  
dc.description.fil
Fil: Aistleitner, Christoph. Technical University Graz; Austria  
dc.description.fil
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  
dc.description.fil
Fil: Scheerer, Adrian-Maria. Technical University Graz; Austria  
dc.description.fil
Fil: Slaman, Theodore A.. University of California at Berkeley; Estados Unidos  
dc.journal.title
Acta Arithmetica  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.4064/aa170213-5-8  

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