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

  • Theta inversion
  • Number field
  • Quadratic reciprocity
  • Algebraic number theory

• Graduation date

  2017-11

• 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.