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On Mobius orthogonality for interval maps of zero entropy and orientation-preserving circle homeomorphisms
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2015 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 53, no 2, 317-327 p.Article in journal (Refereed) Published
Abstract [en]

We will prove Sarnak's conjecture on Mobius disjointness for continuous interval maps of zero entropy and also for orientation-preserving circle homeomorphisms by reducing these result to a well-known theorem of Davenport from 1937.

Place, publisher, year, edition, pages
2015. Vol. 53, no 2, 317-327 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-173755DOI: 10.1007/s11512-014-0208-5ISI: 000360305500007Scopus ID: 2-s2.0-84940582441OAI: oai:DiVA.org:kth-173755DiVA: diva2:855996
Note

QC 20150923

Available from: 2015-09-23 Created: 2015-09-18 Last updated: 2017-12-01Bibliographically approved
In thesis
1. Certain results on the Möbius disjointness conjecture
Open this publication in new window or tab >>Certain results on the Möbius disjointness conjecture
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

We study certain aspects of the Möbius randomness principle and more specifically the Möbius disjointness conjecture of P. Sarnak. In paper A we establish this conjecture for all orientation preserving circle homeomorphisms and continuous interval maps of zero entropy. In paper B we show, that for all subshifts of finite type with positive topological entropy the Möbius disjointness does not hold. In paper C we study a class of three-interval exchange maps arising from a paper of Bourgain and estimate its Hausdorff dimension. In paper D we consider the Chowla and Sarnak conjectures and the Riemann hypothesis for abstract sequences and study their relationship.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2017. 30 p.
Series
TRITA-MAT-A, 2017:05
Keyword
Dynamical Systems, Ergodic Theory, Number Theory
National Category
Natural Sciences
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-215682 (URN)978-91-7729-561-7 (ISBN)
Public defence
2017-11-03, F3, Kungl Tekniska högskolan, Lindstedtsvägen 26,, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

QC 20171016

Available from: 2017-10-16 Created: 2017-10-12 Last updated: 2017-10-16Bibliographically approved

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  • apa
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More styles
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  • nn-NB
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  • Other locale
More languages
Output format
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