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dc.contributor.author
Burrin, Claire
dc.contributor.author
Shapira, Uri
dc.contributor.author
Yu, Shucheng
dc.date.accessioned
2021-03-10T15:12:50Z
dc.date.available
2021-01-19T12:29:07Z
dc.date.available
2021-03-10T15:12:50Z
dc.date.issued
2020-09-28
dc.identifier.uri
http://hdl.handle.net/20.500.11850/463723
dc.description.abstract
We study the limiting distribution of the rational points under a horizontal translation along a sequence of expanding closed horocycles on the modular surface. Using spectral methods we confirm equidistribution of these sample points for any translate when the sequence of horocycles expands within a certain polynomial range. We show that the equidistribution fails for generic translates and a slightly faster expanding rate. We also prove both equidistribution and non-equidistribution results by obtaining explicit limiting measures while allowing the sequence of horocycles to expand arbitrarily fast. Similar results are also obtained for translates of primitive rational points.
en_US
dc.language.iso
en
en_US
dc.publisher
Cornell University
en_US
dc.title
Translates of rationals along expanding closed horocycles on the modular surface
en_US
dc.type
Working Paper
ethz.journal.title
arXiv
ethz.pages.start
2009.13608v1
en_US
ethz.size
49 p.
en_US
ethz.identifier.arxiv
2009.13608
ethz.publication.place
Ithaca, NY
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::08802 - Iozzi, Alessandra (Tit.-Prof.)
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::08802 - Iozzi, Alessandra (Tit.-Prof.)
en_US
ethz.date.deposited
2021-01-19T12:29:15Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Metadata only
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ethz.rosetta.installDate
2021-03-10T15:13:02Z
ethz.rosetta.lastUpdated
2021-03-10T15:13:02Z
ethz.rosetta.versionExported
true
ethz.COinS
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