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COMPLETENESS OF THE LIST OF SPINOR REGULAR TERNARY QUADRATIC FORMS

Part of: Forms and linear algebraic groups

Published online by Cambridge University Press:  05 December 2018

A. G. Earnest  and
Anna Haensch
A. G. Earnest
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, IL 62901, U.S.A. email aearnest@siu.edu
Anna Haensch
Affiliation:
Department of Mathematics and Computer Science, Duquesne University, Pittsburgh, PA 15282, U.S.A. email haenscha@duq.edu
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Abstract

Extending the notion of regularity introduced by Dickson in 1939, a positive definite ternary integral quadratic form is said to be spinor regular if it represents all the positive integers represented by its spinor genus (that is, all positive integers represented by any form in its spinor genus). Jagy conducted an extensive computer search for primitive ternary quadratic forms that are spinor regular, but not regular, resulting in a list of 29 such forms. In this paper, we will prove that there are no additional forms with this property.

MSC classification

Primary: 11E20: General ternary and quaternary quadratic forms; forms of more than two variables 11E12: Quadratic forms over global rings and fields

Information

Type
Research Article
Information
Mathematika , Volume 65 , Issue 2 , 2019 , pp. 213 - 235
Copyright
Copyright © University College London 2018 

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Footnotes

The research of the second author was supported by an Association for Women in Mathematics Mentoring Travel Grant.

References

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