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Low-lying geodesics in an arithmetic hyperbolic three-manifold

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TitleInfo
Title
Low-lying geodesics in an arithmetic hyperbolic three-manifold
Name (type = personal)
NamePart (type = family)
McKeon
NamePart (type = given)
Katie Lynn
NamePart (type = date)
1990-
DisplayForm
Katie Lynn McKeon
Role
RoleTerm (authority = RULIB)
author
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NamePart (type = family)
Kontorovich
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Alex
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Alex Kontorovich
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Advisory Committee
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chair
Name (type = personal)
NamePart (type = family)
Iwaniec
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Henryk
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Henryk Iwaniec
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Advisory Committee
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internal member
Name (type = personal)
NamePart (type = family)
Tunnell
NamePart (type = given)
Jerrold
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Jerrold Tunnell
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Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Pierce
NamePart (type = given)
Lillian
DisplayForm
Lillian Pierce
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
outside member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
School of Graduate Studies
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
Genre (authority = ExL-Esploro)
ETD doctoral
OriginInfo
DateCreated (qualifier = exact)
2018
DateOther (qualifier = exact); (type = degree)
2018-10
CopyrightDate (encoding = w3cdtf)
2018
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
We examine closed geodesics in the quotient of hyperbolic three space by the discrete group of isometries SL(2,Z[i]). There is a correspondence between closed geodesics in the manifold, the complex continued fractions originally studied by Hurwitz, and binary quadratic forms over the Gaussian integers. According to this correspondence, a geodesic is called fundamental if the associated binary quadratic form is. Using techniques from sieve theory, symbolic dynamics, and the theory of expander graphs, we show the existence of a compact set in the manifold containing infinitely many fundamental geodesics.
Subject (authority = RUETD)
Topic
Mathematics
Subject (authority = ETD-LCSH)
Topic
Three-manifolds (Topology)
Subject (authority = ETD-LCSH)
Topic
Geodesics (Mathematics)
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
RelatedItem (type = host)
TitleInfo
Title
School of Graduate Studies Electronic Theses and Dissertations
Identifier (type = local)
rucore10001600001
Identifier
ETD_9109
Identifier (type = doi)
doi:10.7282/t3-cj23-rp08
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electronic resource
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application/pdf
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text/xml
Extent
1 online resource (76 pages) : illustrations
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Katie Lynn McKeon
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
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Rights

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The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
McKeon
GivenName
Katie
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2018-07-22 21:07:10
AssociatedEntity
Name
Katie McKeon
Role
Copyright holder
Affiliation
Rutgers University. School of Graduate Studies
AssociatedObject
Type
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Name
Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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Technical

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2018-07-22T20:35:38
DateCreated (point = end); (encoding = w3cdtf); (qualifier = exact)
2018-07-22T20:35:38
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