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Refinements of Selberg's sieve
Descriptive
TypeOfResource
Text
TitleInfo
(ID = T-1)
Title
Refinements of Selberg's sieve
Identifier
ETD_2562
Identifier
(type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000053287
Language
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eng
Genre
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theses
Subject
(ID = SBJ-1)
Name
(authority = LC-NAF)
NamePart
(type = personal)
Selberg, Atle
Subject
(ID = SBJ-2);
(authority = RUETD)
Topic
Mathematics
Subject
(ID = SBJ-3);
(authority = ETD-LCSH)
Topic
Selberg trace formula
Subject
(ID = SBJ-4);
(authority = ETD-LCSH)
Topic
Sieves (Mathematics)
Abstract
(type = abstract)
This thesis focuses on refinements of Selberg's sieve as well as new applications of the sieve. Sieve methods are addressed in four ways. First, we look at lower bound sieves. We will construct new lower bound sieves that give us non-trivial lower bounds for our sums. The lower bound sieves we construct will give better results than those previously known. Second, we create an upper bound sieve and use it to bound the number of primes to improve Selberg's version of the Brun-Titchmarsh Theorem. We improve a constant in the bound of the number of primes in an arbitrary interval of fixed length. Third, we construct an upper bound sieve to improve the large sieve inequality in special cases. Sieve methods allow us to improve this well-known bound of exponential sums. Finally, we include some notes on the use of successive approximations to give a choice of an upper bound sieve that minimizes the main term and the remainder term simultaneously.
PhysicalDescription
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electronic resource
Extent
vi, 69 p.
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application/pdf
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text/xml
Note
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Ph.D.
Note
Includes abstract
Note
Vita
Note
(type = bibliography)
Includes bibliographical references
Note
(type = statement of responsibility)
by Sara Elizabeth Blight
Name
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Blight
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Sara Elizabeth
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1983-
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author
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Sara Blight
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Iwaniec
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Henryk
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chair
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Henryk Iwaniec
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(type = family)
Weibel
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Charles
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internal member
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Advisory Committee
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Charles Weibel
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NamePart
(type = family)
Miller
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Stephen
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internal member
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Advisory Committee
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Stephen Miller
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Chamizo
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Fernando
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outside member
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Advisory Committee
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Fernando Chamizo
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NamePart
Rutgers University
Role
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degree grantor
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Graduate School - New Brunswick
Role
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school
OriginInfo
DateCreated
(qualifier = exact)
2010
DateOther
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(type = degree)
2010
Place
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(type = code)
xx
RelatedItem
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier
(type = RULIB)
ETD
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(type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier
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rucore19991600001
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NjNbRU
Identifier
(type = doi)
doi:10.7282/T35T3KJ8
Genre
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ETD doctoral
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Rights
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The author owns the copyright to this work.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
RightsHolder
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(type = personal)
Name
FamilyName
Blight
GivenName
Sara
Role
Copyright Holder
RightsEvent
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Type
Permission or license
DateTime
2010-04-09 13:08:25
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Name
Sara Blight
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.
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Technical
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ETD
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application/pdf
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application/x-tar
FileSize
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378880
Checksum
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272e3cac89165d1283f7d9d0805454f8281e409c
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