On primitively universal quadratic forms
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In 1999, Manjul Bhargava proved the Fifteen Theorem and showed that there are exactly 204 universal positive definite integral quaternary quadratic forms. We consider primitive representations of quadratic forms and investigate a primitive counterpart to the Fifteen Theorem. In particular, we give an efficient method for deciding whether a positive definite integral quadratic form in four or more variables with odd square-free determinant is almost primitively universal.
Keywordsalmost primitively universal quadratic forms p-adic symbols
MSC11E20 11E25 11E08 11E99
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