Enumeration of quadratic forms over totally real fields
- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- Paula J. Hamby (Creator)
- Institution
- The University of North Carolina at Greensboro (UNCG )
- Web Site: http://library.uncg.edu/
- Advisor
- Dan Yasaki
Abstract: Let F be a real quadratic field with OF its ring of integers. Let f be a quadratic form over F with discriminant D. Using Koecher Theory and the generalized Voronoï Algorithm, we show that there are finitely many quadratic forms with discriminant D over F. As there are finitely many quadratic forms, we can enumerate the forms up to a factor of the determinant of the norm of the form. As an application, we can use these results to show a correspondence between the class of quadratic forms over F and the ideal class of a relative extension of F generated by the field discriminant.
Enumeration of quadratic forms over totally real fields
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Created on 12/1/2012
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Additional Information
- Publication
- Thesis
- Language: English
- Date: 2012
- Keywords
- Koecher, Quadratic Form, Reduction Theory, Totally Real Field, Voronoi
- Subjects
- Forms, Quadratic
- Quadratic fields
- Algebraic number theory