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The number of lattice points in irrational polytopes
Descriptive
TitleInfo
Title
The number of lattice points in irrational polytopes
Name
(type = personal)
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Borda
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Bence
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(type = date)
1985-
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Bence Borda
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author
Name
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Beck
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Jozsef
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Jozsef Beck
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Advisory Committee
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chair
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Iwaniec
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Henryk
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Henryk Iwaniec
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Advisory Committee
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internal member
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Kopparty
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Swastik
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Swastik Kopparty
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Advisory Committee
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internal member
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Bumby
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Richard
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Richard Bumby
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Advisory Committee
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outside member
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Rutgers University
Role
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degree grantor
Name
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Graduate School - New Brunswick
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school
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Text
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theses
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2016
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2016-05
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2016
Place
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xx
Language
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eng
Abstract
(type = abstract)
The discrepancy | t P ∩ Z^d | - lambda (P) t^d is studied as a function of the real variable t>1, where P is a polytope in R^d with at least one vertex not in Z^d. For a special class of cross polytopes and orthogonal simplices defined in terms of algebraic numbers the discrepancy is proved to be the sum of an explicit polynomial of t and a randomly fluctuating term of smaller order of magnitude. This phenomenon has not yet been described in the literature for any convex body. A general discrepancy bound is proved for polytopes the coordinates of the vertices of which all belong to a given real quadratic field. As a corollary a new property of the regular dodecahedron is obtained. Finally, answering a question of Beck, a formula is given for the variance of a random fluctuation arising in a lattice point counting problem on the plane. The main methods used are Fourier analysis and the theory of Diophantine approximation.
Subject
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Topic
Mathematics
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
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ETD
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ETD_7042
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electronic resource
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application/pdf
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text/xml
Extent
1 online resource (v, 113 p. : ill.)
Note
(type = degree)
Ph.D.
Note
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Includes bibliographical references
Subject
(authority = ETD-LCSH)
Topic
Lattice theory
Subject
(authority = ETD-LCSH)
Topic
Polytopes
Note
(type = statement of responsibility)
by Bence Borda
RelatedItem
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TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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NjNbRU
Identifier
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doi:10.7282/T36D5W4J
Genre
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ETD doctoral
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Rights
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The author owns the copyright to this work.
RightsHolder
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Name
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Borda
GivenName
Bence
Role
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Permission or license
DateTime
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2016-02-22 18:18:54
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Name
Bence Borda
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Affiliation
Rutgers University. Graduate School - New Brunswick
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License
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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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windows xp
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1.5
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2016-01-25T12:57:25
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2016-01-25T12:57:25
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