Title:
Positive-definite-n-regular-quadratic-forms
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Description: Apositive definite integral quadratic form f is called n-regular if f represents every quadratic form of rank n that is represented by the genus
of f . In this paper, we show that for any integer n greater than or equal to 27, every n-regular (even) form f is (even) n-universal, that is, f represents all (even, respectively) positive definite integral quadratic forms of rank n. As an application, we show that the minimal rank of n-regular forms has an
exponential lower bound for n as it increases.
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Positive definite n-regular quadratic forms.pdf
