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

  • Author / Creator
    Morrill, Ryan W
  • 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.

  • Subjects / Keywords
  • Graduation date
    2017-11:Fall 2017
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R3GQ6RG41
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. 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.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Patnaik, Manish (Mathematics)
  • Examining committee members and their departments
    • Liu, Andy (Mathematis)
    • Prus-Czarnecki, Andrezj (Physics)
    • Cliff, Gerald (Mathematics)