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The Kloosterman circle method and weighted representation numbers of positive definite quadratic forms
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Jones, Edna Luo.
The Kloosterman circle method and weighted representation numbers of positive definite quadratic forms.
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https://doi.org/doi:10.7282/t3-122z-r222
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Description
Title
The Kloosterman circle method and weighted representation numbers of positive definite quadratic forms
Name
Jones, Edna Luo (author)
;
Kontorovich, Alex (chair)
;
Iwaniec, Henryk (member)
;
Miller, Stephen D (member)
;
Vaughan, Robert C (member)
;
Rutgers University
;
School of Graduate Studies
Date Created
2022
Other Date
2022-10 (degree)
Subject
Mathematics
,
Kloosterman circle method
,
Nonstationary phase
,
Number theory
,
Positive definite quadratic forms
,
Weighted representation number
Extent
1 online resource (145 pages)
Description
We develop a version of the Kloosterman circle method with a bump function that is used to provide asymptotics for weighted representation numbers of positive definite integral quadratic forms. Unlike many applications of the Kloosterman circle method, we explicitly state some constants in the error terms that depend on the quadratic form. This version of the Kloosterman circle method uses Gauss sums, Kloosterman sums, SaliƩ sums, and a principle of nonstationary phase. We briefly discuss a potential application of this version of the Kloosterman circle method to a proof of a strong asymptotic local-global principle for certain Kleinian sphere packings.
Note
Ph.D.
Note
Includes bibliographical references
Genre
theses
Persistent URL
https://doi.org/doi:10.7282/t3-122z-r222
Language
English
Collection
School of Graduate Studies Electronic Theses and Dissertations
Organization Name
Rutgers, The State University of New Jersey
Rights
The author owns the copyright to this work.
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