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dc.contributor.author
Simon, Valérie
dc.contributor.author
Cesaratto, Eda
dc.contributor.author
Rotondo, Pablo
dc.contributor.author
Safe, Martin Dario
dc.date.available
2023-12-14T15:06:28Z
dc.date.issued
2023-04
dc.identifier.citation
Simon, Valérie; Cesaratto, Eda; Rotondo, Pablo; Safe, Martin Dario; Lochs-type theorems beyond positive entropy; Springer Wien; Monatshefete Fur Mathematik; 200; 4; 4-2023; 737-779
dc.identifier.issn
0026-9255
dc.identifier.uri
http://hdl.handle.net/11336/220374
dc.description.abstract
Lochs’ theorem and its generalizations are conversion theorems that relate the number of digits determined in one expansion of a real number as a function of the number of digits given in some other expansion. In its original version, Lochs’ theorem related decimal expansions with continued fraction expansions. Such conversion results can also be stated for sequences of interval partitions under suitable assumptions, with results holding almost everywhere, or in measure, involving the entropy. This is the viewpoint we develop here. In order to deal with sequences of partitions beyond positive entropy, this paper introduces the notion of log-balanced sequences of partitions, together with their weight functions. These are sequences of interval partitions such that the logarithms of the measures of their intervals at each depth are roughly the same. We then state Lochs-type theorems which work even in the case of zero entropy, in particular for several important log-balanced sequences of partitions of a number-theoretic nature.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer Wien
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
CHANGE OF BASE
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FAREY AND STERN–BROCOT SEQUENCES
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INFINITE ENTROPY
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LOCHS’ THEOREM
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NUMERATION SYSTEMS
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THREE-DISTANCE THEOREM
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ZERO ENTROPY
dc.subject.classification
Matemática Pura
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Matemáticas
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CIENCIAS NATURALES Y EXACTAS
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Otras Ciencias de la Computación e Información
dc.subject.classification
Ciencias de la Computación e Información
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Lochs-type theorems beyond positive entropy
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2023-12-14T12:53:07Z
dc.journal.volume
200
dc.journal.number
4
dc.journal.pagination
737-779
dc.journal.pais
Austria
dc.description.fil
Fil: Simon, Valérie. Centre National de la Recherche Scientifique; Francia
dc.description.fil
Fil: Cesaratto, Eda. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
dc.description.fil
Fil: Rotondo, Pablo. Université Gustave Eiffel; Francia
dc.description.fil
Fil: Safe, Martin Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
dc.journal.title
Monatshefete Fur Mathematik
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00605-022-01805-y
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