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Two dynamical perspectives on the randomness of the Mobius function

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datacite.rightsopen.access
dc.contributor.advisorSarnak, Peter Cen_US
dc.contributor.authorPeckner, Ryan Nathanielen_US
dc.contributor.otherMathematics Departmenten_US
dc.date.accessioned2015-12-07T19:51:18Z
dc.date.accessioned2026-09-30T11:31:16Z
dc.date.available2015-12-07T19:51:18Z
dc.date.available2026-09-30T11:31:16Z
dc.date.issued2015en_US
dc.description.abstractSarnak's approach to the Mobius randomness heuristic from the standpoint of dynamical systems is studied in two complementary settings. First, the Mobius function is realized in the context of symbolic dynamics, and we prove that its associated squarefree factor has a unique measure of maximal entropy. We then show that the Mobius function is linearly disjoint from all zero-entropy translations on homogeneous spaces of connected Lie groups, generalizing work of Vinogradov, Green-Tao, and Bourgain- Sarnak-Ziegler.en_US
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/dsp01v979v546w
dc.identifier.urihttps://theses-dissertations.princeton.edu/handle/88435/dsp01v979v546w
dc.language.isoenen_US
dc.publisherPrinceton, NJ : Princeton Universityen_US
dc.relation.isformatofThe Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: http://catalog.princeton.edu/en_US
dc.subject.classificationMathematicsen_US
dc.titleTwo dynamical perspectives on the randomness of the Mobius functionen_US
dc.typeAcademic dissertations (Ph.D.)en_US
dspace.entity.typePublication
pu.projectgrantnumber690-2143en_US

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