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)
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/
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.

Additional Information

Language: English
Date: 2012
Koecher, Quadratic Form, Reduction Theory, Totally Real Field, Voronoi
Forms, Quadratic
Quadratic fields
Algebraic number theory

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