Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
On certain aspects of the Möbius randomness principle
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). (Dynamical Systems)
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper we study different aspects of the Möbius randomness principle. We rephrase the Chowla, Sarnak conjectures and the Riemann hypothesis for abstract sequences and study their relationships. We, in particular, show, that in this setting the Chowla and Sarnak conjectures do not imply the Riemann hypothesis. In the second part of the paper we also study the connection between the multiplicative and additive van der Corput criteria.

Keyword [en]
Number Theory, Dynamical Systems
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-215736OAI: oai:DiVA.org:kth-215736DiVA, id: diva2:1149254
Note

QC 20171016

Available from: 2017-10-13 Created: 2017-10-13 Last updated: 2017-10-16Bibliographically 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. p. 30
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

Open Access in DiVA

fulltext(361 kB)24 downloads
File information
File name FULLTEXT01.pdfFile size 361 kBChecksum SHA-512
d46db3c466f315c1faddea93637b471fa21366c603a5a680ea38cc788772b94d9ccae039a46a9e8f3195c916d47e97bab352bf2fc5241bcfa690a2c80628eacf
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Karagulyan, Davit
By organisation
Mathematics (Dept.)
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 24 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 76 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf