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The 15 theorem states that if an integral quadratic form with integral matrix represents the numbers 1, 2, 3, 5, 6, 7, 10, 14, 15, then it represents all numbers. Is there an analogue of this theorem for cubic forms?

Thomas
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  • The 15 theorem is about positive-definite quadratic forms. This doesn't have a direct analogue for cubic forms. In fact, there are lots of features of quadratic forms that don't carry over to cubic forms (e.g., diagonalizability over the base field or interesting structure for its orthogonal group). Is there a reason you think there ought to be an analogue, or is this question asked for the sake of curiosity? – KCd Jan 18 '14 at 00:51
  • I just thought it would be nice if there was a way to easily prove that cubic forms represent all numbers. – Thomas Jan 18 '14 at 02:15

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