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Permanent link (DOI): https://doi.org/10.7939/R3GQ6RG41

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Theta Inversion and The Law of Quadratic Reciprocity for Arbitrary Number Fields Open Access

Descriptions

Other title
Subject/Keyword
algebraic number theory
quadratic reciprocity
number field
theta inversion
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Morrill, Ryan W
Supervisor and department
Patnaik, Manish (Mathematics)
Examining committee member and department
Liu, Andy (Mathematis)
Prus-Czarnecki, Andrezj (Physics)
Cliff, Gerald (Mathematics)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2017-07-27T09:33:46Z
Graduation date
2017-11:Fall 2017
Degree
Master of Science
Degree level
Master's
Abstract
In this thesis, we formulate and prove the theorem of quadratic reciprocity for an arbitrary number field. We follow Hecke and base our argument on analytic techniques and especially on an identity of theta functions called theta inversion. From this inversion formula and a limiting argument, we obtain an identity of Gauss sums which is central to our proof of quadratic reciprocity. The statement of the law of quadratic reciprocity in this generality contains unevaluated Gauss sums which we will make explicit in some examples.
Language
English
DOI
doi:10.7939/R3GQ6RG41
Rights
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
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